The International Symposium on Lattice Field Theory is an annual conference series that attracts scientists from around the world working on lattice quantum field theory. The conference is the largest in the field and covers topics in
In recent years there has been much progress on the investigation of the QCD phase diagram with lattice QCD. This talk will focus on the developments in the last few years. Especially the addition of external influences and extended ranges of $T$ and $\mu$ yield an increasing number of interesting results, a subset of which will be discussed. Many of these conditions are important for the understanding of both the QCD transition in the early universe and heavy ion collision experiments which are conducted for example at the LHC and RHIC. This offers many exciting opportunities for comparisons between theory and experiment.
New incarnations of heavy-ion collision experiments are turning our attention to hard processes and a more fine-grained resolution of the QGP. In this endeavor quarkonia or open heavy flavors turn out to be versatile probes, which are usually described through models based on perturbative QCD, AdS, and effective field theories. The lattice provides nonperturbative input and constraints to such models.
In-medium bottomonia, the complex static quark-antiquark potential, and the heavy-quark momentum diffusion coefficient are key quantities where lattice gauge theory has recently achieved significant progress with impact for heavy-ion phenomenology.
I review these lattice results, relate them to phenomenological applications, and close with a outlook.
We discuss recent progress in Tensor Lattice Field Theory and economical, symmetry preserving, truncations suitable for quantum computations/simulations. We focus on spin and gauge models with continuous Abelian symmetries such as the Abelian Higgs model and emphasize noise-robust implementations of Gauss's law. We discuss recent progress concerning the comparison between field digitizations and character expansions, symmetry breaking in tensor language, wave-packet preparation and possible new implementations of Abelian models using Rydberg atoms.
The paradigm of effective field theory is one of the most powerful tools available in physics. While most commonly employed in parametrizing renormalization group flow, it is also of great utility in describing dispersive systems such as $K_0 - \bar{K}_0$ states that both oscillate and decay. Of particular interest for the lattice community is the study of field theories off the real axis of coupling constants. This is important for behavior at finite chemical potential as well as in the study of critical phenomena more generally. These models can exhibit a rich phenomenology, such as non-unitary critical points and steady-state attractors. We describe a mapping of an arbitrary dispersive bosonic lattice effective theory onto a class of unitary system + environment models that are amenable to simulation on quantum machinery, and discuss how certain aspects can be studied even on near-term noisy hardware.
Some aspects of quantum systems with non-unitary dynamics are well-described by non-Hermitian effective Hamiltonians. Such systems contain a wealth of interesting physics such as their phase structure, eg. QCD at finite Baryon density, which describes cores of neutron stars. Classical simulation of general non-Hermitian Hamiltonians is rendered difficult, and in some cases, impossible due to the sign problem. Quantum computers offer the promise of solving this issue, but contemporary quantum computers in the Noisy Intermediate Scale Quantum (NISQ) era are not capable of simulating complicated field theories. Simpler, open field theories on small lattices, with the axiom of locality/sparsity, however, are amenable for simulation on near-term devices. We simulate non-unitary dynamics by embedding the system of interest in a larger unital one via ancillary qubits and use measurements on the ancillas to extract the desired dynamics. The price of doing this are the inevitable quantum jumps, which put the system in an error state. In this talk, two measurement-based prescriptions will be presented for simulating general non-Hermitian Hamiltonians. We apply these quantum channels to the well-studied 1-D quantum Ising chain with an imaginary longitudinal magnetic field and show that the channels are sensitive to the exceptional points, which in the thermodynamic limit corresponds to the Lee-Yang Edge singularity, despite quantum jumps.
Open lattice field theories are useful in describing many physical systems. Yet their implementation in traditional quantum computing is hindered by the requirement of Hermiticity. One method used to overcome this is embedding the non-Hermitian system within a larger Hermitian system by introducing ancillary qubits. We implement the transverse Ising Model with an addition of an imaginary longitudinal magnetic field. We show for two-qubit systems this method works very well. For larger systems in the NISQ era, a robust noise model is needed. We investigate the robustness to noise of this methodology for larger quantum systems using a QISKIT-based noise model.
The possibility for near-term quantum simulations in lattice field theory depends upon efficiently using the limited resources available. In this talk, we will discuss how approximating lattice gauge theories like SU(3) with discrete subgroups can be theoretically analyzed as a lattice effective field theory. Further, methods for implementation upon quantum hardware will be covered. Numerical results for Euclidean calculations for U(1) and SU(3) subgroups will be presented with modified and improved actions that relate to Hamiltonians other than Kogut-Susskind's.
The Schwinger model is a testbed for the study of quantum gauge field theories. We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In particular, we analyze low-order Trotter formula simulations of the Schwinger model, using recently derived commutator bounds, and give upper bounds on the resources needed for simulations. We give scalable measurement schemes and algorithms to estimate observables which we cost in both settings by assuming a simple target observable: the mean pair density. Finally, we bound the root-mean-square error in estimating this observable via simulation as a function of the diamond distance between the ideal and actual CNOT channels. This work provides a rigorous analysis of simulating the Schwinger model, while also providing benchmarks against which subsequent simulation algorithms can be tested.
Computing conformal dimensions $D(j_L,j_R)$ of local fields that transform in an irreducible representation of $SU(2) \times SU(2)$ labeled with $(j_L,j_R)$ at the $O(4)$ Wilson-Fisher fixed point has become interesting recently, especially when $j_L$, $j_R$ become large. These calculations are challenging in the traditional lattice $O(4)$ model. We can overcome these difficulties by using a qubit regularized O(4) model constructed with a local five dimensional Hilbert space. While previously we computed $D(j,j)$ using this approach, here we design an algorithm to compute $D(j,j-1)$ for $2 \leq j \leq 20$.
We provide strong evidence that the asymptotically free (1+1)-dimensional non-linear O(3) sigma model can be regularized using a quantum lattice Hamiltonian, referred to as the "Heisenberg-comb", that acts on a Hilbert space with only two qubits per spatial lattice site. The Heisenberg-comb consists of a spin-half anti-ferromagnetic Heisenberg-chain coupled anti-ferromagnetically to a second local spin-half particle at every lattice site. Using a world-line Monte Carlo method we show that the model reproduces the universal step-scaling function of the traditional model up to correlation lengths of 200,000 in lattice units and argue how the continuum limit could emerge. We provide a quantum circuit description of time-evolution of the model and argue that near-term quantum computers may suffice to demonstrate asymptotic freedom.
Excited state contamination is one of the most challenging sources of systematics to tackle in the determination of nucleon matrix elements and form factors.
The signal-to-noise problem prevents one from considering large source-sink time separations.
Instead, state-of-the-art analyses consider multi-state fits.
Excited state contributions to the correlation functions are particularly significant in the axial channel.
In this work, we confront the problem directly.
Since the major source of contamination is understood to be related to pion production, we consider 3-point correlators with a $N$ operator at the source and a $N \pi$ interpolating operator at the sink, which allows studies of $N \to N\pi$ matrix elements.
After discussing the challenges that arise when using a 2-particle interpolating operator, like the projection onto the proper irreducible representation and on the isospin components, we present results of $N \to N\pi$ processes, mediated by an axial current, on an $m_{\pi} \approx 420 MeV$ ensemble.
Using an SU(3) flavour symmetry breaking expansion between the strange and light quark masses, we determine how this constrains the extrapolation of baryon and meson octet matrix elements and form factors. In particular we can construct certain combinations, which fan out from symmetric point (when all the quark masses are degenerate) to the point when the light and strange quarks take their physical values. As an example we consider vector form factors at various momentum.
We report on the recent progress of our analysis into nucleon sigma terms, as well as the singlet axial and tensor nucleon charges. These are extracted from the CLS gauge configurations, which utilise the Lüscher-Weisz gluon action and the Sheikholeslami-Wohlert fermion action with $N_f = 2 + 1$ fermions, with pion masses ranging from the physical value up to 410 MeV, and lattice spacings covering a range between 0.09fm and 0.04fm. We have employed a variety of methods to determine the necessary correlation functions, including the sequential source method for connected contributions, and the truncated solver method for disconnected contributions. Extrapolation to the physical point involves leading order discretisation, chiral, and finite-volume effects.
Preliminary results are presented for nucleon isovector charges and twist-2 matrix elements which have been obtained employing an improved analysis strategy to deal with excited state contamination. The set of CLS N_f=2+1 gauge ensembles in this study has been extended compared to our 2018 calculation, including an ensemble at physical quark masses. Besides the addition of new ensembles, the number of gauge configurations and measurements has been increased on several of the existing ensembles and the analysis has been extended to include additional source-sink separations. The ensembles cover a range of the light quark mass corresponding to $M_\pi\approx 0.130\mathrm{MeV} \ldots 350\mathrm{MeV}$, four values of the lattice spacing $a\approx0.05\mathrm{fm}\ldots 0.09\mathrm{fm}$ and a large range of volumes. Results at the physical point are computed for each observable from a combined chiral, continuum and finite size extrapolation.
We present updates on the calculation of flavor diagonal axial, tensor and scalar nucleon charges $g_{A,S,T}^{u,d,s}$ focusing on understanding the excited state contamination (ESC) including contributions of possible low-lying ($N\pi$ and $N\pi\pi$) excited states to individual nucleon matrix elements.
Starting with a summary of our studies of the sensitivity of various charges and form factors to the excited state spectrum, including input from PCAC, vector meson dominance and chiral perturbation theory, I will present an update on results for nucleon charges and form factors.
In this talk, I will discuss our recent calculations (Phys. Rev. D102 (2020) no.5, 054512, JHEP 2104 (2021) 044 ) of the first x-moment of nucleon isovector polarized, unpolarized and transversity distributions (momentum fraction, helicity and transversity moment respectively). We use the standard method for the calculation of these moments (via matrix elements of twist two operators), we carry out a detailed analysis of the sources of systematic uncertainty, in particular of excited state contributions. Our calculations have been performed using two different lattice setups (Clover on HISQ and Clover on Clover), each with several ensembles, which give consistent results that are in agreement with global fit analyses.
We have implemented and are computing nucleon 3pt functions using the stochastic Laplacian Heaviside (sLapH) method. Such a technique enables the use of momentum space creation and annihilation operators providing access to the Breit-Frame as well as full control of the spin of the initial and final operator. It also enables the use of multi-hadron operators, for example the problematic N-pi excited state. We will report on the success (or lack thereof) of using sLapH for such three point function calculations as measured both in terms of the computational cost, the stochastic signal that is achievable as compared to the more standard fixed source-sink separation computations using local creation operators and momentum space sinks.
The broad class of U(N) and SU(N) Polyakov loop models on the lattice
are solved exactly in the combined large N, Nf limit, where N is a number
of colors and Nf is a number of quark flavors, and in any dimension.
In this 't Hooft-Veneziano limit the ratio N/Nf is kept fixed. We calculate
both the free energy and various correlation functions. The critical behavior
of the models is described in details at finite temperatures and non-zero baryon
chemical potential. Furthermore, we prove that the calculation of the N-point
(baryon) correlation function reduces to the geometric median problem in
the confinement phase. In the deconfinement phase we establish an existence
of the complex masses and an oscillating decay of correlations in a certain
region of parameters.
We consider a dual representation of an effective three-dimensional Polyakov loop model for the SU(3) theory at nonzero real chemical potential. This representation is free of the sign problem and can be used for numeric Monte-Carlo simulations. These simulations allow us to locate the line of second order phase transitions, that separates the region of first order phase transition from the crossover one. The behavior of local observables in different phases of the model is studied numerically and compared with predictions of the mean-field analysis. Our dual formulation allows us to study also Polyakov loop correlation functions. From these results, we extract the screening masses and compare them with the large-N predictions.
In the strong coupling and heavy quark mass regime, lattice QCD reduces to a 3 dimensional theory of Polyakov loops. We apply coarse graining techniques to such theories in 1 and 2 dimensions at finite temperature and non-zero chemical potential.
In 1 dimension the method is applied to the effective theory up to $\mathcal{O}(\kappa^4)$, where $\kappa$ is the hopping parameter of the original Wilson action. Using the transfer matrix, the recursion relations are solved analytically. The thermodynamic limit is taken for some intensive observables. Afterwards, continuum extrapolation is performed numerically and results are discussed.
In 2 dimensions the coarse graining method is applied in the pure gauge and static quark limit. Running couplings are obtained and the fixed points of the transformations are discussed. Finally, the critical coupling of the deconfinement transition is determined in both limits. Agreement to about $15\%$ with Monte Carlo results from the literature is observed.
We present generalizations of Hamiltonian Lattice QCD as derived from the continuous time limit of strong coupling lattice QCD: we discuss the flavor dependence and the effect of gauge corrections. This formalism is applied at finite temperature and baryon density and allows both for analytic and numeric investigations that are sign problem-free.
QCD at fixed baryon number can be formulated in terms of transfer matrices explicitly defined in the canonical sectors. In the heavy-dense limit, the fermionic contributions to the canonical partition functions can be calculated analytically in terms of Polyakov loops. It turns out that at low temperatures and infinitely strong coupling the sign problem is exponentially reduced by many orders of magnitude for any baryon number, that is, essentially absent. We show how this can be used for the construction of cluster algorithms which achieve a similar improvement away from the strong coupling limit.
Thimble regularisation of Yang Mills theories is still to a very large extent terra incognita. We will discuss a couple of topics related to this big issue. 2d YM theories are in principle good candidates as a working ground. An analytic solution is known, for which one can switch from a solution in terms of a sum over characters to a form which is a sum over critical points. We would be interested in an explicit realisation of this mechanism in the lattice regularisation, which is actually quite hard to work out. A second topic is the inclusion of a topological term in the lattice theory, which is the prototype of a genuine sign problem for pure YM fields. For both these challenging problems we do not have final answers. We will present the current status of our study.
The low-lying Dirac modes become localised at the finite-temperature transition in QCD and in other gauge theories, suggesting a general connection between their localisation and deconfinement. The simplest model where this connection can be tested is $\mathbb{Z}_2$ gauge theory in 2+1 dimensions. We show that in this model the low modes in the staggered Dirac spectrum are delocalised in the confined phase and become localised in the deconfined phase. We also show that localised modes correlate with disorder in the Polyakov loop configuration, in agreement with the "sea/islands picture" of localisation. These results further support the conjecture that localisation and deconfinement are closely related.
We report results on symmetries of temporal correlators above Tc
obtained within the N_F = 2 QCD with the chirally symmetric
Dirac operator at physical quark masses. We observe both U(1)_A
and SU(2)_L * SU(2)_R chiral symmetries as well as the chiral
spin symmetry SU(2)_CS, which is a symmetry of the color charge
and of the electric interaction. Emmergence of the latter
symmetry suggests that above Tc but below roughly 3Tc the color
charge is not yet screened and degrees of freedom are the chirally
symmetric quarks bound by the electric field into the color singlet
objects.
The leading hadronic vacuum polarisation contribution to $(g-2)_\mu$
was recently determined by the Budapest-Marseille-Wuppertal
collaboration to sub-percent precision, providing for the first
time an ab-initio calculation of this quantity with errors comparable
to phenomenological determinations.
To reach this unprecedented level of precision, a number of
critical issues needed to be addressed. One such issue was
the significant finite-size effects arising from the two-pion
physics that dominates the hadronic vacuum polarisation.
In this talk we describe how these finite-size effects were
addressed through a combination of dedicated lattice simulations,
chiral perturbation theory, and phenomenological models.
In this talk we present in detail the continuum extrapolation procedure of the
recent determination of the leading order hadronic vacuum polarization contribution to the muon anomalous magnetic moment from the Budapest-Marseille-Wuppertal collaboration (arxiv:2002.12347).
We present an update, from the Fermilab Lattice, HPQCD, and MILC collaborations, of our results for the light-quark, connected contribution to the hadronic vacuum polarization correction to the muon’s anomalous magnetic moment. The calculation is performed on 2+1+1 highly-improved staggered quark (HISQ) ensembles with physical pion mass at four lattice spacings (0.15fm-0.06fm). We also present preliminary results for a study of the two-pion contributions to the vector-current correlation function performed on the 0.15fm ensemble.
We present updated results for the light-quark connected part of the leading hadronic contribution to the muon g−2 from configurations with 2+1+1 flavors of HISQ quarks using the time-momentum representation of the electromagnetic current correlator. We have added statistics on two ensembles as well as a fourth lattice spacing using configurations that have been generated by the MILC collaboration at the physical pion mass. Additionally we account for the leading finite-volume and taste-breaking effects using Staggered Chiral Perturbation Theory at NNLO.
Recently, the hadronic vacuum polarization contribution to the anomalous
magnetic moment of the muon was determined by the BMW collaboration with
sub-percent precision. Such a precision requires to
control many sources of uncertainty. One of these is the uncertainty
in the determination of the lattice spacing.
In this talk, we present the scale setting entering this computation. It
relies on the mass of the Omega baryon as input which is directly used to set
the scale of our main calculation. It also allows us to calculate the
value of the intermediate scale setting quantity $w_0$. Here, we present
our calculation of this quantity with a relative precision of about 0.4%.
The infamous strong CP problem in particle physics can in principle be solved by a massless up quark. In particular, it was hypothesized that topological effects could substantially contribute to the observed nonzero up-quark mass without reintroducing CP violation. Alternatively to previous work using fits to chiral perturbation theory, in this talk we present direct lattice QCD computations of the topological mass contribution, based on examining the dependence of the pion mass on the dynamical strange-quark mass. We find that the size of the topological mass contribution is inconsistent with the massless up-quark solution to the strong CP problem.
Proton decay is a long-sought manifestation of baryon number violation predicted by Grand Unification and expected due to baryon asymmetry of the Universe. Amplitudes of such decay in various channels depend on proton structure determined by nonperturbative QCD dynamics and have to be determined on a lattice. We report results of a recent calculation of these amplitudes using chirally symmetric quark action at the physical pion mass. While our lattices relatively coarse (a=0.2 and 0.14 fm), we don't observe any significant lattice spacing dependence.
In recent years, lattice determinations of non-perturbative quantities such as $f_K$ and $f_\pi$, which are relevant for $V_{us}$ and $V_{ud}$, have reached an impressive precision of O(1%) or better. To make further progress, electromagnetic and strong isospin breaking effects must be included in lattice QCD simulations.
We present the status of the RBC&UKQCD lattice calculation of isospin-breaking corrections to light meson leptonic decays. This computation is performed in a (2+1)-flavor QCD+QED using Domain Wall Fermions with near-physical quark masses. The QED effects are implemented via a perturbative expansion of the action in $\alpha$. In this calculation, we work in the electro-quenched approximation and the photons are implemented in the Feynman gauge and QEDL formulation.
We present results for $\eta$ and $\eta^\prime$ masses at the physical point.
The two independent decay constants, e.g., for the flavour singlet/non-singlet
basis, are also computed for both particles. The chiral and continuum limit extrapolation is performed on 21 CLS $n_f = 2+1$ Wilson Clover improved ensembles at four different lattice spacings and along two quark mass trajectories, including one ensemble very close to the physical quark mass point. For the first time the decay constants are determined directly from the
axialvector matrix elements without model assumptions. This allows us to
study the QCD scale dependence of the decay constants and to determine all low
energy constants contributing at NLO in Large-$N_c$ ChPT at a well defined
renormalization scale.
We present results of gluonic and pseudoscalar matrix elements of the $\eta$ and $\eta'$ mesons at the physical quark mass point, in the continuum limit. The simulations are carried out on $n_f=2+1$ CLS ensembles, with non-perturbatively improved Wilson fermions. We discuss the renormalization of these quantities and check the consistency with the singlet and non-singlet axial Ward identities. Our results are well described in terms of Large-$N_c$ ChPT at NLO. We comment on phenomenological applications.
We measure the spatial distribution of all components of the color fields surrounding a static quark–antiquark pair in QCD with (2+1) HISQ flavors.
We isolate the nonperturbative component of the longitudinal chromoelectric
color field responsible for the linear term in the confining potential.
It has long been known that there is a phase transition between confined and unconfined phases of compact pure gauge QED on the lattice. In this work we report three manifestations of this phase change as seen in the Landau gauge photon propagator, the static potential, and distribution of Dirac Strings in the gauge fixed configurations. Each of these was calculated with large lattices with volumes: $32^4$, $48^4$ and $96^4$. We will show that the confined phase manifests with a Yukawa type propagator with a dynamically generated mass gap, a linearly increasing potential, and a significant concentration of Dirac strings while the unconfined phase appears consistent with the continuum results, a free propagator, a near constant long-distance potential, and a small concentration of Dirac strings trending towards 0. Furthermore, the photon propagator is investigated near the transition between the two phases.
We present a major update on the spectrum of the closed flux-tube in $D=3+1$ $SU(N)$ gauge theories. Namely, we calculate the excitation spectrum of a confining flux-tube which winds around a spatial torus as a function of its length $l$, for short as well as long tubes. We do so for $N=3,5,6$ and two different values of the lattice spacing. Our states are characterised by the quantum numbers of spin $J$, transverse parity $P_{\perp}$, longitudinal parity $P_{\parallel}$ as well as by the longitudinal momentum $p_{\parallel}$. Our extended basis of operators used in combination with the generalized eigenvalue method enables us to extract masses for all irreducible representations characterised by $\{ J,P_{\perp},P_{\parallel} \}$.
We confirm that most of the low-lying states are well described by the spectrum of the Goddard–Goldstone–Rebbi–Thorn string. In addition we provide strong evidence, that in addition to string like states, massive modes exist on the bulk. More precisely the ground state with quantum numbers $J^{P_{\perp}, P_{\parallel}}=0^{--}$ exhibits a behaviour which is in agreement with the interpretation of being an axion on the wordsheet of the flux-tube. This state arises from a topological interaction term included in the effective world-sheet action. In addition we observe that the second excited state with $J^{P_{\perp}, P_{\parallel}}=0^{++}$ behaves as a massive mode with mass twice that of the axion.
Pure gauge theories are rather different from theories with pure scalar and fermionic matter, especially in terms of the nature of excitations. For example, in scalar and fermionic theories, one can create ultra-local excitations. For a gauge theory, such excitations need to be closed loops that do not violate gauge invariance. In this talk, we present a study on the condensation phenomenon associated with the stringy excitations of an Abelian lattice gauge theory. These phenomena are studied through numerical simulations of a U(1) quantum link model in 2+1 dimensions in a ladder geometry using matrix product states. We will give a numerical demonstration of the presence of the string excitations in the ground states.
Confinement remains one the most interesting and challenging nonperturbative phenomenon in non-Abelian gauge theories. Recent semiclassical (for $SU(2)$) and lattice (for QCD) studies have suggested that confinement arises from interactions of statistical ensembles of instanton-dyons with the Polyakov loop. In this talk, I will present recent work which has extended the study of semiclassical ensemble of dyons to the $SU(3)$ Yang-Mills theory. It will be shown that such interactions do generate the expected first-order deconfinement phase transition. The properties of the ensemble, including the dyon correlations and densities, and the topological susceptibility, are studied over a range of temperatures above and below $T_c$. Additionally, the dyon ensemble is studied in the Yang-Mills theory containing an extra trace-deformation term. It will be shown that such a term causes the theory to remain confined even at high temperatures.
We show that in the vicinity of the deconfinement transition the behaviour of the interquark potential in pure lattice gauge theories can be precisely predicted combining results from Conformal Field Theory, Effective String Theory and Integrable Models. We compare these predictions with simulations of the SU(2) gauge model both in (2+1) and in (3+1) dimensions.
The gauge-invariant formulations of lattice field theories provide a way to study real-time dynamics using a smaller effective Hilbert space. This allows for more information to be encoded for the same quantum resources as a non-gauge invariant forumlation which will be important for simulations on Noisy Intermediate Scale Quantum (NISQ) computers. While qubit-based hardware is currently the most widely available, it does not naturally reflect the Hilbert spaces of complicated quantum field theories. Qudits (n-state objects) provide a more natural description of the Hilbert spaces. The purely bosonic nature of Compact Scalar Quantum Electrodynamics (csQED) provides a nice test-bed for qudit based digitizations and truncations of continuous symmetries. We will discuss the methods of digitizing csQED for qudit-based quantum computers, the robustness to different types of noise balanced with accuracy of field truncations.
Quantum technologies offer the prospect to efficiently simulate sign-problem afflicted phenomena, such as topological terms, chemical potentials, and out-of-equilibrium dynamics. In this work, we derive the 3+1D topological $\theta$-term for Abelian and non-Abelian lattice gauge theories in the Hamiltonian formulation, paving the way towards Hamiltonian-based simulations of such terms on quantum and classical computers. We further study numerically a 3+1D U(1) lattice gauge theory with the $\theta$-term via exact diagonalization. Our results suggest the occurrence of a phase transition at constant values of $\theta$, as indicated by an avoided level-crossing and abrupt changes in the plaquette expectation value, the electric energy density, and the topological charge density.
In order to simulate quantum field theories using quantum computers, a regularization of the target space of the field theory must be obtained which admits a representation in terms of qubits. For the 1+1 dimensional nonlinear sigma model, there have been several proposals for how such a regularization may be achieved. The fuzzy sphere regularization proposes to represent the Hilbert space of the NLSM by a truncation of the noncommutative 2-sphere, a truncation which nonetheless preserves the continuous O(3) symmetry of the theory. In this talk, we discuss an attempt to demonstrate that this regularization reproduces the same physics as the O(3) sigma model using the machinery of matrix product states.
Quantum simulation has the promise of enabling access to Minkowski-time dynamical observables in quantum field theories. Progress in devising and benchmarking quantum-simulation proposals, in form of analog protocols or digital algorithms, is ongoing, and increasingly complex theories are being targeted towards the goal of simulating QCD. In this talk, I will introduce a hybrid analog-digital simulation scheme for studying bosonic field theories coupled to matter, such as the Yukawa theory and the 1+1 dimensional QED, by taking advantage of both bosonic degrees of freedom (phonons) and spin degrees of freedom (internal states of the ions) in a trapped-ion quantum simulator. It will be shown that significant improvement is anticipated in the simulation resource requirement, i.e., the number of qubits and entangling operations, when compared with the fully-digital algorithms, while the flexibility of a digital scheme in engineering a complex Hamiltonian is maintained. This motivates near-term implementations that can supersede both the fully digital and fully analog implementations of the same theories.
We introduce a new method to calculate phase shifts on noisy intermediate scale quantum (NISQ) hardware platforms using a wave packet edge time delay. The method uses the early and intermediate stages of the collision because the standard method based on the asymptotic out-state behavior is unreachable using today’s NISQ platforms. The calculation was implemented on a 4-site transverse Ising model in one spatial dimension with and without a potential interaction. A time evolution operator describing the progression of the system was constructed and transmission and reflection coefficients were calculated based on the identified quantum Fourier transformed momentum states. The detailed analysis of the phase shift calculations on both IBM superconducting transmon and University of Maryland ion trap quantum computers shows the platform independence of the methodology. This successful implementation of this wave packet preparation and projection on momentum eigenstates can now be performed with actual quantum computing hardware platforms. This method provides a procedure for calculating phase shifts and opens the possibility of using noisy intermediate scale quantum devices to perform real-time quantum mechanics and quantum field theory scattering calculations.
Dimensionally reducing gauge theories like QED or Yang-Mills theory on small spatial tori often yields simple quantum mechanical models that retain some of the interesting structure of the parent gauge theory. 2D electrodynamics with massive charge-N matter, for example, leads to the quantum mechanics of a particle on a circle with a Z_N potential and a theta-term. This model, despite being simple to solve, exhibits the ’t Hooft anomaly or global inconsistency of the parent theory, and related phenomena of spontaneous symmetry breaking and instanton-anti-instanton interference. We propose a scheme for realizing the real-time quantum simulation of this model on a synthetic dimension. Similar phenomena in more complicated theories are of great interest and may be studied by quantum simulators in the future.
Future quantum computers may serve as a tool to access non-perturbative real-time correlation functions. In this talk, we discuss the prospects of using these to study Compton scattering for arbitrary kinematics. In particular, the need to restrict the size of the spacetime in quantum computers prohibits a naive determination of such amplitudes. However, we present a practical solution to this challenge that may allow for future determinations of deeply virtual Compton scattering amplitudes, as well as many other reactions that are presently outside the scope of standard lattice QCD calculations.
We present a complete and scalable quantum algorithm for the simulation of SU(2) gauge bosons coupled to fermionic matter in one spatial dimension. To represent the gauge fields, we find it is more practical to start from their Schwinger boson formulation, rather than the more conventional Kogut-Susskind rigid rotor formulation. Within this framework, and taking Trotter-Suzuki decomposition as the time evolution scheme, we then construct explicit circuits for the simulation of the three types of terms found in the Hamiltonian: electric energy, fermion mass energy, and the gauge-matter interaction. We comment on the similarities and differences relative to simulating the U(1) analogue of this theory, the Schwinger model, which is discussed in another talk by A.F. Shaw.
We will present the current status of nucleon structure studies with physical light quarks ($m_\pi$ = 135 MeV) in a large spatial extent of about 10 fm. Our calculations are carried out with the PACS10 gauge configurations generated by the PACS Collaboration with the stout-smeared O(a) improved Wilson fermions and Iwasaki gauge action at $\beta$=1.82 corresponding to the lattice spacing of 0.084 fm. In this talk, we mainly focus on the lower moments of nucleon structure functions that are known as quark momentum and helicity fractions respectively, which are regarded as bench marks on lattice calculations of parton distribution functions.In addition, we will present the preliminary results with another PACS10 ensemble generated at finer lattice spacing.
We highlight QCDSF/UKQCD Collaboration's recent developments on computing the Compton amplitude directly via an implementation of the second-order Feynman-Hellmann theorem. As an application, we compute the nucleon Compton tensor across a range of photon momenta at an unphysical quark mass. This enables us to study the $Q^2$ dependence of the low moments of the nucleon structure functions in a lattice calculation for the first time. We present some selected results for the moments of the $F_1$, $F_2$ and $F_L$ structure functions and discuss their implications.
Lattice QCD calculations of the nucleon electromagnetic form factors are of interest at the high and low momentum transfer regions. For high momentum transfers especially there are open questions, such as the zero crossing in the proton's electric form factor, which require more calculations. We will present recent progress from the QCDSF/UKQCD/CSSM collaboration on the calculations of these form factors using the Feynman-Hellmann method in lattice QCD. This method provides an efficient method allowing us to reach high momentum transfers. In this talk we present results of the form factors up to 9 GeV$^{2}$, using N$_{f}$=2+1 flavour fermions for three different pion masses in the range 310-470 MeV. The results are extrapolated to the physical point through the use of a flavour breaking expansion at two different values of the lattice spacing, allowing for a study of discretisation effects.
We report on the use of Feynman-Hellmann techniques to calculate the off-forward Compton amplitude (OFCA) in lattice QCD. At leading-twist, the Euclidean OFCA is parameterised by moments of generalised parton distributions (GPDs). Hence this calculation provides the opportunity to determine GPD-related quantities from first principles.
Determining the existence and the location of the QCD critical point remains a major open problem, both theoretically and experimentally. In this talk, I present a new way of reconstructing the equation of state in the vicinity of the nearest singularity (the Lee-Yang edge singularity in the crossover region) from a truncated Taylor series expansion for small $\mu$. This is done by using a combination of Pad\'e resummation and conformal/uniformization maps. Then, I show that this information can be used to (i) determine the location of the critical point and (ii) constrain the non-universal mapping parameters between the Ising and QCD equations of state.
I explicitly demonstrate these ideas in the 2d Gross-Neveu model whose phase diagram shares the key aspects of the conjectured QCD phase diagram including the existence of a critical point.
Chromo-electric screening at high temperature is encoded in the large distance behavior of Polyakov loop correlators. In SU(N) gauge theory (quenched QCD) the large distance behavior of the Polyakov loop correlators has been studied and the corresponding chromo-electric screening length has been determined. In QCD with light dynamical quarks this turned out to be very difficult because of the large Monte-Carlo noise. We study the long distance behavior of the correlator of the real and imaginary part of the Polyakov loop in 2+1 flavor QCD with nearly physical quark masses using HISQ action and lattices with temporal extent $N_t=6,~8,~10$ and $12$. To reduce the noise we apply several levels of HYP smearing to the Polyakov loops and determine the corresponding chromo-electric screening masses. We compare our results to the weak coupling calculations at high temperatures.
We report on the preliminary studies of static quark anti-quark potential at non-zero temperature in 2+1 flavor QCD using 96^3x32 lattices with lattice spacing a=0.03fm, physical strange quark mass and light quark masses corresponding to pion mass of about 300 MeV. The static potential is obtained from Wilson line correlator in Coulomb gauge with additional HYP smearing to reduce the noise at large quark anti-quark separations. We apply 0, 5 and 10 steps of HYP smearing to ensure that there is no physical effect from oversmearing. We obtain the complex static potential at non-zero temperature by assuming a single peak plus continuum form of the spectral function. Furthermore, the continuum part of the spectral function is constrained by the T=0 calculations at the same lattice spacing. The peak position gives the real part of the potential, while the width of the peak gives the imaginary part.
The sequential melting of the bottomonia states is one of the important signals for the existence of a Quark Gluon Plasma. The study of bottomonia spectral functions on the lattice is a difficult task for many reasons. Calculations based on NRQCD, that are commonly used for such purpose, are not applicable at high temperatures. In this work we propose a new method to study this problem by calculating the spatial screening masses of bottomonia states. We calculate the spatial meson correlators and extract the screening masses for mesons in different quantum channels using highly improved staggered quark (HISQ) action for bottom quarks and dynamical 2+1 flavor QCD HISQ gauge configurations. The typical lattice we choose are of size $N_s^3\times N_\tau$ where $N_s=4 N_\tau$ and $N_\tau=8,10, 12$. We consider the temperature range $T=300$-$1100$ MeV. We show that for $T>500$ MeV the temperature dependence of the screening masses of the ground state bottomonia are compatible with the expectations based on uncorrelated quark-antiquark pairs.
We report our study on critical endpoints of finite temperature phase transitions in (2+1)- and 4-flavor QCD with Wilson-Clover fermions. As an extension of our previous calculations on coarser lattices, we performed our simulations on lattices with temporal extents of 8 and 10 for 2+1 and 4 flavors, respectively, to carry out continuum extrapolations more precisely. For the calculation in (2+1)- flavor QCD, as a first step, we fixed $\beta$ and $\kappa_s$ values to 1.75 and 0.133000, respectively, and varied $\kappa_l$, where we found that the phase transition seems to be of first order. In 4 flavor QCD we tried to determine a location of the critical endpoint from calculations at various combinations of $\beta$ and $\kappa$ values with three different spatial volumes. The finite size scaling of chiral susceptibility under the assumption of three-dimensional Z(2) universality suggests that the critical endpoint exists around $\beta$ = 1.65.
Understanding of the QCD phase diagram is one of important topics in nuclear and hadron physics.
In particular, various possible phase structures are proposed from analyses of effective theories in low temperature and high density region. One of them is inhomogeneous chiral condensate which exhibits characteristic space structures. Since there is no general established method for determination of the structure of the chiral condensate, usually some solutions such as chiral spiral and kink solutions are assumed. On the other hand, the Monte Carlo method in lattice QCD does not work in the low temperature and high density region, because of existent of the notorious sing problem. However, the usual lattice calculation is applicable to the 1+1 Gross-Neveu (GN) model and chiral GN model that have similar property of QCD, since they do not have the sign problem at finite density. Recently the interesting phase structure of the inhomogeneous chiral condensate in the 1+1 dimensional GN model on the lattice has been presented [1].
Here we study the phase structure of the 1+1 dimensional chiral GN model, performing the lattice simulation. Advantage of using the Monte Carlo method is that one can investigate the general space structure of the sigma and pion condensates without any assumption of it. We will discuss the phase diagram of the chiral GN model with finite number of flavors, comparing that of the GN model with finite number of flavors.
[1] J. Lenz, L. Pannullo, M. Wagner et al., Phys. Rev. D 101, no.9, 094512 (2020).
We give a new description to obtain the shear viscosity at finite temperature.
Firstly, we obtain the correlation function of the renormalized energy-momentum tensor using the gradient flow method.
Secondly, we estimate the spectral function from the smeared correlation functions
using the sparse modeling method.
The combination of these two methods looks promising to determine the shear viscosity precisely.
We present a lattice QCD calculation of the axial $\gamma$W-box diagrams relevant for the kaon semilep-leptonic decays. We utilize a recently proposed method, which connects the electroweak radiative corrections in Sirlin's representation to that in chiral perturbation theory. It allows us to use the axial $\gamma$W-box correction in the SU(3) limit to obtain the low energy constants for chiral perturbation theory. From first principles our results confirm the previously used low energy constants provided by the minimal resonance model with a significant reduction in uncertainties.
We calculate the $B\to D^{(*)}\ell\nu$ form factors in 2+1 flavor
relativistic lattice QCD by employing the Moebius domain-wall action
for all quark flavors. Our simulations are carried out at lattice cut-offs
$a^{-1} \sim 2.5$, 3.6 and 4.5 GeV with varying bottom quark masses
up to 0.7 $a^{-1}$ to study heavy quark mass dependence and
discretization effects. We extrapolate the form factors
to the continuum limit and physical quark masses, and make a comparison
in the differential decay rate with experiment.
We present preliminary results for the kaon semileptonic form factors
using one of the PACS10 configuration sets, whose physical volume is
(10.2 fm)$^4$ at the physical point with the lattice spacing of 0.064 fm.
The configuration was generated using the Iwasaki gauge action and $N_f=2+1$
stout-smeared clover quark action. The value of |$V_{us}$| is determined
using the interpolated result of the form factors to the zero momentum
transfer. Our value of |$V_{us}$| is compared with a prediction of the standard
model from the unitarity triangle and recent lattice results.
We also show a preliminary result of |$V_{us}$| in the continuum limit
obtained from analysis using the preliminary result of 0.064 fm combined
with our previous result at the coarser lattice spacing of 0.085 fm.
Two important sources of systematic errors in lattice QCD calculations of radiative leptonic decays are unwanted exponentials in the sum over intermediate states and unwanted excited states created by the meson interpolating field. Performing the calculation using a 3d sequential propagator allows for better control over the systematic uncertainties from intermediate states, while using a 4d sequential propagator allows for better control over the systematic uncertainties from excited states. We calculate form factors using both methods and compare how reliably each controls these systematic errors. We also employ a hybrid approach involving global fits to data from both methods. I will present our results comparing these methods for both heavy and light mesons.
We calculate $K \to \pi\pi$ matrix elements using periodic boundary conditions as an independent calculation from our previous calculation with G-parity boundary conditions. We present our preliminary results for physical masses on a $24^3, a^{-1}=1$ GeV, $2+1$-flavor Mobius DWF ensemble generated by the RBC and UKQCD collaborations and discuss the prospect for high-precision computation of $\epsilon'$ with periodic boundary conditions.
Observation of neutrinoless double-beta $(0\nu\beta\beta)$ decay, a beyond the standard model process that violates lepton number conservation, would imply that neutrinos are Majorana fermions. In order to draw reliable conclusions from the current experimental limits and potential future discoveries, it is important to reduce the uncertainties in the theoretical predictions of its decay rate. A major contribution to these uncertainties comes from the effective field theories (EFT) matched ab initio nuclear many-body calculation of its nuclear matrix element. It was pointed out recently that the leading order EFT amplitude of the subprocess $nn\to pp(ee)$ in the simplest scenario of light neutrino exchange remains undetermined due to an unknown contribution from a newly identified short-range operator. Lattice quantum chromodynamics (LQCD) is the only way to directly and reliably determine the associated low-energy constant. We provide here a formalism to obtain the physical $nn\to pp(ee)$ decay amplitude, and hence the missing contribution, from the LQCD calculation of the correlation function for this process. The complications arising from the Euclidean and finite-volume nature of the corresponding correlation functions are fully resolved, and the result of this work, therefore, can be readily employed in the ongoing LQCD studies of this process.
We present results for the neutron electric dipole moment due to the to dimension 4 and dimension 6 gluonic CP violation, and the isovector quark chromoelectric dipole moment using clover valence quarks on HISQ dynamical ensembles. For the gluonic operators, we use the gradient flow scheme to obtain divergence-free continuum results. For the chromoelectric dipole moment operator, we use the unflowed local operator but discuss how the quadratically divergent mixing with the pseudoscalar operator can be controlled non-perturbatively. The connection to the continuum is done using horizontal matching at tadpole-improved tree-level and leading-log running.
We will present preliminary findings on improving the lattice calculation of the neutron electric dipole moment from the θ term in QCD. The neutron EDM is highly correlated with the lowest lying modes of the Dirac operator. We take advantage of this with a full volume sampling for the low mode part of the quark propagator in order to increase statistics. This augments the all-mode averaging technique using a large number of sources for each configuration. We use the method of measuring the energy shift of the two-point correlation function in a uniform background electric field. Initial results are for a $16^3 \times 32$ ensemble of domain-wall fermions at $m_{\pi}$ = 420 MeV.
Hamiltonian formulation of lattice gauge theories provides the natural framework for the purpose of quantum simulation, an area of research that is growing with advances in quantum-computing algorithms and hardware. It is therefore important to identify the most accurate, while computationally economic, Hamiltonian formulation(s) of lattice gauge theories along with necessary truncation imposed on the Hilbert space of gauge bosons for any finite computing resources. We report a study toward addressing this question in the case of non-Abelian lattice gauge theories that require the imposition of non-Abelian Gauss's laws on the Hilbert space.
Quantum link models (QLMs) are extensions of Wilson-type lattice gauge theories, and show rich physics beyond the phenomena of conventional Wilson gauge theories. Here we explore the physics of U(1) symmetric QLMs, both using a more conventional quantum spin-1/2 representation, as well as a fermionic representation. In 2D, we show that both bosonic and fermionic QLMs have the same physics. We then explore the models in 3D and find different behavior for the two QLMs. For the bosons, we see evidence for a quantum phase transition from a broken phase to a quantum spin liquid, but for the fermions, we identify not one but two distinct phases in addition to the fermionic broken phase. We explore the symmetries of the ground state in the broken phase strong coupling limit, and explain the spectrum for both models. The phase transitions are confirmed through scaling of the gaps as well as the ground state fidelity susceptibilities.
In the Hamiltonian formulation, free spin-1/2 massless Dirac fermions on a bipartite lattice have an $O(4)$ (spin-charge) symmetry. Lattice interaction terms usually break this symmetry down to some subgroups. For example, the Hubbard interaction at half-filling breaks the symmetry down to $SO(4)$ by breaking the spin-charge flip symmetry. In this work, we construct a lattice model with a new interaction $V$, which is similar to the Hubbard interaction, but preserves the spin-charge flip symmetry. Using perturbative calculations in the continuum, we compute the RG flow diagram with both $U$ and $V$ interactions and show the existence of a spin-charge flip symmetric fixed point that can be studied by tuning the coupling $V$ at $U=0$. In particular we show that this fixed point is different from the one reached by tuning the Hubbard coupling $U$. Monte Carlo calculations using the fermion bag idea can help us compute the critical exponents at the spin-charge flip symmetric fixed point.
In the Hamiltonian picture, free spin-1/2 Dirac fermions on a bipartite lattice have an O(4) (spin-charge) symmetry. Here we construct an interacting lattice model with an interaction V, which is similar to the Hubbard interaction but preserves the spin-charge flip symmetry. By tuning the coupling V, we show that we can study the phase transition between the massless fermion phase at small V and a massive fermion phase at large V. We construct a fermion bag algorithm to study this phase transition and find evidence for it to be second order. Perturbative calculations show that the universality class of the transition is different from the one studied earlier involving the Hubbard coupling U. Here we obtain some critical exponents using lattices up to L=48.
I present lattice Monte Carlo evidence of localized quantum excitations of the fields surrounding static electric charges in the q=2 abelian Higgs model; such excitations would appear as excited states of isolated fermions. Since the q=2 abelian Higgs model is a relativistic version of the Landau-Ginzburg effective model of superconductivity, these results may have some application in a condensed matter context.
To investigate the properties of the large $N$ limit of $\mathcal{N}=1$ SUSY Yang-Mills theory, we have started a feasibility study for a reduced matrix model with an adjoint Majorana fermion. The gauge action is based on the Wilson action and the adjoint-fermion is the Wilson-Dirac action on a reduced lattice with twisted gauge boundary condition. We employ the RHMC algorithm in which the absolute value of the Pfaffian is incorporated. The sign of the Pfaffian is involved with the re-weighting method and separately measured as an observable. In this talk, we show the configuration generation status towards the large $N$ limit and the behavior of the lowest/lower eigenvalue(s) of the Wilson-Dirac fermion operator.
The Lorentzian type IIB matrix model is a promising candidate for a non-perturbative formulation of superstring theory. In previous studies, Monte Carlo calculations provided interesting results indicating the spontaneous breaking of SO(9) to SO(3) and the emergence of (3+1)-dimensional space-time. However, an approximation was used to avoid the sign problem, which seemed to make the space-time structure singular. In this talk, we report our results obtained by using the complex Langevin method to overcome the sign problem instead of using this approximation. In particular, we discuss the emergence of continuous space-time in a new phase, which we discovered recently.
The type IIB matrix model was proposed as a nonperturbative formulation of superstring theory in 1996. We simulate this model by applying the complex Langevin method to overcome the sign problem. Here, we clarify the relationship between the Euclidean and Lorentzian versions of the type IIB matrix model in a new phase we discovered recently.
When non-Abelian gauge fields in $SU(3)$ QCD have a line-singularity leading to non-commutability with respect to successive partial-derivative operations, the non-Abelian Bianchi identity is violated. The violation as an operator is shown to be equivalent to violation of the Abelian-like Bianchi identities. Then there appear eight Abelian-like conserved magnetic monopoles of the Dirac type in $SU(3)$ QCD. Using lattice Monte-Carlo simulations, perfect Abelian and monopole dominances are shown to exist without introducing additional smoothing techniques like partial gauge fixings when we define lattice Abelian-like monopoles following the DeGrand-Toussaint method adopted in the study of the Dirac monopole in lattice compact QED. As reported separately, the Abelian dual Meissner effect around a pair of static quark and antiquark is caused by the solenoidal Abelian monopole current.
Lattice gauge scalar models allow analytical connection between confinement region and Higgs region for gauge invariant operators.
Combining the cluster expansion and the duality, we try to understand non-trivial contribution from scalar field in quark confinement mechanism.
In order to understand quark confinement further, moreover, we study double-winding Wilson loop averages in the analytical region on the phase diagram.
We propose a subvolume method to study the $\theta$ dependence of the free
energy density of the four-dimensional SU($N$) Yang-Mills theory on the lattice.
As an attempt, the method is first applied to SU(2) Yang-Mills theory at
$T=1.2\,T_c$ to understand the systematics of the method. We then proceed to
the calculation of the vacuum energy density and obtain the $\theta$ dependence,
at least, to $\theta\sim\pi$. The numerical results combined with the theoretical
requirements provide the evidence for the spontaneous CP violation at $\theta = \pi$,
which is in accordance with the large $N$ prediction and in contrast to the CP$^1$
model in two dimensions.
We present a lattice QCD calculation of the energy eigenvalues of the dibaryon system using the gauge ensembles generated with the domain wall fermion action. Using the sparsening field method, multiple dibaryon interpolating operators are used to reduce the contamination from excited states. Some relevant results for the weak transition matrix elements of the dibaryon system are also shown.
In this work we study the large $N_c$ scaling of pion-pion scattering lengths for $N_f=4$ degenerate quark flavours. We focus on the standard isospin-2 channel and the adjoint-antisymmmetric representation, which is unique for $N_f \geq 4$. We compare the results obtained for two regularisations (Wilson and Twisted-Mass) and three values of the lattice spacing, and observe significant discretisation effects in the AA channel. Finally, we compare our results to NLO SU(4) and NNLO U(4) Chiral Perturbation Theory and study the $N_c$ scaling of the relevant low-energy couplings.
Finite-volume scattering at physical pion mass is still an exploratory field in lattice QCD. This generally involves the extraction of excited states through multi-particle correlators on systems with resonances. In that context, distillation has demonstrated to be effective both as a smearing kernel and a computational tool. Motivated by the study of the smearing profile of the distillation operator, we compare stochastic and exact distillation cases for different numbers of Laplacian eigenvectors using a RBC-UKQCD $N_f=2+1$ domain-wall fermion lattice with a physical pion mass.
The scattering length is an important quantity that describes scattering at low energies. We will present our evaluation of the $K\pi$ scattering length in the isospin $I=\frac12$ and $I=\frac32$ channels. The computation uses the RBC-UKQCD 2+1-flavour ensembles with Domain Wall Fermions at near-physical quark masses. With the help of all-to-all methods, we construct the correlation functions, and we handle excited states and round-the-world effects to obtain a stable result.
We present a finite volume spectroscopy calculation of I=1 pi-pi scattering utilizing the (stochastic) distillation framework on close to physical and physical point N_f = $2+1$ CLS ensembles. Using the finite volume energy levels, we discuss the long-distance behavior of the vector correlator, which is dominated by the two-pion channel. This part can be accurately constrained using the reconstructions, which has important consequences for lattice calculations of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment.
We numerically investigate different techniques to extract scattering amplitudes from a Euclidean Lattice $\phi^4$ theory with two fields having different masses. We present an exploratory study of a recently proposed method by Bruno and Hansen for extracting the scattering length from a four-point function (cf. arXiv:2012.11488) and a study of the two and three particle quantization condition.
We present a lattice QCD study of $\pi-N$ scattering in the iso-spin $I=3/2$ channel.
The calculation is performed using $N_f=2+1+1$ flavors of twisted mass fermions including an ensemble with
physical pion mass. We compute energy levels for all the moving frames with total momentum up to $\vec{P}=2\pi L(1,1,1)$,
and for all the relevant irreducible representation of the lattice symmetry groups.
We perform a phase-shift analysis including $S$ and $P$ wave phase shifts assuming a Breit-Wigner form of the resonance
in order to determine the parameters of the $\Delta$ resonance.
In their seminal publication of 1990, Maiani and Testa showed that physical amplitudes away from threshold cannot be directly extracted (i.e. without analytically continuing or solving an inverse problem), from infinite-volume Euclidean correlators. As a result, in realistic lattice calculations, the limited knowledge of correlation functions on finite subsets of points allows only for the extraction of approximate smeared spectral densities (or else amplitudes via finite-volume energies). In this presentation we discuss the recent results obtained in arXiv:2012.11488, which extend the original work of Maiani and Testa and relate it to spectral reconstruction methods.
The quantization of the energy levels of interacting two-particle system in a finite volume has been well considered in which the exponential suppressed finite volume effect was usually omitted. The partial waving mixing effect in the finite volume is also an obstacle to extracting the interacting information in the infinite volume. In this work, we propose a framework to calculate the energy levels of two-particle systems in the box with the plane wave basis expansion rather than the partial wave expansion. We can reduce the interacting matrices of operators into the irreducible representations of the corresponding point groups. We use a nonrelativistic toy model and a relativistic example, $\pi\pi$ scattering, to illustrate the framework for both static and moving systems. In this framework, the exponential suppressed effect and partial wave mixing effect are embedded naturally. Our results show that the exponential suppression effect and the partial wave mixing effect for NN interaction with typical range $1/m_\pi$ are important for the box with size L<5 fm. This framework could be used to obtain the two-body finite volume energy spectrum from the effective field theories, unitarization approaches and other theoretical models, which could be related to the lattice QCD raw data.
We investigate the two-flavour Schwinger model in the canonical formulation with fixed fermion number. We use Wilson fermions on the lattice and present a formalism which describes the Dirac operator with dimensionally reduced canonical operators. These reduced operators allow the direct examination of arbitrary meson sectors and the determination of the energy spectrum in each of the sectors. Using Lüscher's finite-volume mass-shift formula we discuss the 1-meson mass as well as the effective 3-meson coupling. From the 2-meson energies we determine the scattering phase shifts and compare the 3-meson energies in the finite volume to predictions based on scattering theory and quantization conditions.
The Hadron Spectrum Collaboration (HSC) presented new results on
two of their ensembles for s-wave scattering phase shifts
in the open-charm sector of QCD. For such ensembles we have made
predictions that are based on the chiral Lagrangian that were published two years ago. In this talk
we confront our phase shifts with those of HSC. A remarkably
consistent picture emerges. In particular there is mounting
evidence for the existence of a flavour sextet state in the $\pi D$
and $\pi D^*$ channels, that show a striking quark-mass dependence.
The measurement of muonic-hydrogen spectroscopy provides the most precise determination of the proton charge radius, where the two-photon exchange contribution plays an important role in the understanding of $\mu$H spectroscopy. We will report a lattice QCD calculation of the two-photon exchange contribution by constructing the proton four-point correlation function.
Nucleon isovector form factors calculated on 2+1-flavor domain-wall fermion (DWF) numerical lattice-QCD ensemble with phyaical up-, down- and strange-quark mass and lattice momentum cut off of about 1.730(4) GeV will be reported.
The electromagnetic polarizability is an important property of nucleon. It describes the response of a nucleon when it is placed in an external electric or magnetic field. The polarizability can be extracted from the real or virtual Compton scattering process $\gamma N \to \gamma N$. We develop a method to calculate the the Compton scattering matrix elements of nucleon from a 4-point correlation function on the lattice. Then we show that the electromagnetic polarizability can be extracted from the lattice data subsequently.
In the analysis of (lattice) QCD observables very often chiral perturbation theory (ChPT) is heavily used to describe the quark mass dependence or relate different observables via symmetry relations. Within ChPT the low energy constants (LECs) play a crucial role and their precise knowledge is important in lattice QCD as well as in phenomenology. While there are many lattice determinations of the LECs in SU(2) ChPT, the SU(3) LECs are less well determined.
We will present our results for the leading order mesonic ($B_0$, $F_0$) and baryonic ($m_0$, $D$, $F$) SU(3) ChPT LECs from $N_f = 3$ flavour lattice QCD. In our study we employ a subset of the $N_f=2+1$ flavour Coordinated Lattice Simulations (CLS) gauge ensembles, denoted as the symmetric line which incorporates exact flavour symmetry, i.e., $m_\ell = m_s$. The ensembles cover a range of different pion masses as well as 6 different lattice spacings and different volumes. This allows us to perform a controlled extrapolation of all LECs to the chiral, infinite volume and continuum limit.
The study of the Compton amplitude has gained attention in recent years. It plays a central role in the analysis of many fundamental problems such as, for example, the evaluation of the Lamb shift in muonic hydrogen, or the calculation of the proton-neutron mass difference. Hence, the calculation of this amplitude on the lattice would definitely contribute to the solution of the above problems. However, lattice results are always plagued by the finite-volume artifacts which may be sizable in some cases. In order to carry out a precise extraction of the Compton amplitude, these finite-volume corrections should be reliably estimated and removed from the lattice data.
Different approaches have been proposed so far for the extraction of the Compton amplitude on the lattice. In this talk, I shall discuss an approach based on the background field method. The calculations are done in Baryon Chiral Perturbation Theory, up-to-and including $O(p^4)$, where $p$ is a small momentum/mass. Our study will be focused on the calculation of the so-called subtraction function, which is related to the Compton amplitude in a particular kinematics. In the beginning, the forward doubly virtual Compton scattering amplitude off nucleons will be evaluated, and the behavior of the subtraction function at small values of the photon momentum will be discussed. Furthermore, the full set of the finite-volume corrections to the subtraction function will be evaluated up-to-and-including $O(p^4)$. It will be shown that, despite the poorly known low-energy constants at this order, the finite-volume artifacts can be evaluated quite accurately and do not preclude one from an accurate measurement of the subtraction function on the lattice.
We compute the quark-connected component of the hadronic vacuum polarization function at the energy scale of the Z boson mass in the Schwinger model. This is done by computing different representations of the Adler function on different energy scales. The mass parameters for the different scales are set with a step scaling scheme in which the lattice spacing and volume are adjusted to the given momentum. At each step the lattice spacing and volume are halved. We perform the continuum limit and investigate the finite volume behavior.
In this talk we present a relativistic and model-independent method to analytically derive electromagnetic finite-size effects beyond the point-like approximation. Structure-dependence appears in terms of physical form-factors and derivatives thereof. The values of these physical quantities can be taken either from experimental measurements or auxiliary lattice calculations. We apply our method to derive the leading structure-dependence in the meson mass, i.e. at order $1/L^3$, and compare to that obtained from non-relativistic effective field theory techniques. In addition, we determine the coefficient of the $1/L^2$-term in leptonic decays of pions and kaons. The knowledge of the latter allows for improved numerical control in extractions of the relevant CKM-matrix elements from lattice QCD+QED.
The nucleon-pion-state contribution to QCD two-point and three-point functions relevant for lattice calculations of the nucleon electromagnetic form factors are studied in chiral perturbation theory.
To leading order the results depend on a few experimentally known low-energy constants only, and the nucleon-pion-state contribution to the form factors can be estimated. The nucleon-pion-state contribution to the electric form factor $G_{\rm E}(Q^2)$ is at the +5 percent level for a source-sink separation of 2 fm, and it increases with increasing momentum transfer $Q^2$. For the magnetic form factor the nucleon-pion-state contribution leads to an underestimation of $G_{\rm M}(Q^2)$ by about 5 percent that decreases with increasing $Q^2$. For smaller source-sink separations that are accessible in present-day lattice simulations the impact is larger, although the ChPT results may not be applicable for such small time separations. Still, a comparison with lattice data at $t\approx 1.6$ fm works reasonably well.
We present results for the isoscalar electromagnetic form factors of the nucleon computed on the CLS ensembles with $N_\mathrm{f} = 2 + 1$ flavors of $\mathcal{O}(a)$-improved Wilson fermions and an $\mathcal{O}(a)$-improved conserved vector current. In order to estimate the excited-state contamination, we investigate several source-sink separations and apply the summation method. For the computation of the quark-disconnected diagrams, a stochastic estimation using the one-end trick is employed. By these means, we obtain a clear signal for the form factors including the quark-disconnected contributions, which have a distinguishable effect on our data.
We consider the chiral Lagrangian with nucleon, isobar, and pion degrees of freedom. The baryon masses and the axial-vector form factor of the nucleon are derived at the one-loop level. We explore the impact of using on-shell baryon masses in the loop expressions. As compared to results from conventional chiral perturbation theory we find significant differences. An application to QCD lattice data is presented. We perform a global fit to the available lattice data sets for the baryon masses and the nucleon axial-vector form factor, and determine the low-energy constants relevant at N$^3$LO for the baryon masses and at N$^2$LO for the form factor. Partial finite-volume effects are considered. We point out that the use of on-shell masses in the loops results in non-analytic behavior of the baryon masses and the form factor as function of the pion mass, which becomes prominent for larger lattice volumes than presently used.
We present the nucleon axial and electromagnetic form factors using $N_\textrm{f}=2+1+1$ twisted mass lattice QCD with clover improvement and with quarks with masses tuned to their physical values. Excited state effects are studied using several sink-source separations in the range 0.8 fm - 1.6 fm, exponentially increasing statistics with the separation such that statistical errors remain approximately constant. In addition, quark disconnected diagrams are included in order to extract the isovector and isoscalar axial form factors and the isospin symmetric proton and neutron electromagnetic form factors, as well as their strange-quark contributions. The radii and moments are extracted by modelling the $Q^2$ dependence, including using the so-called $z$-expansion method. A preliminary assessment of lattice cut-off effects is presented using two lattice spacings directly at the physical point.
We present the analysis of isovector axial vector nucleon form factors for a set of $N_f=2+1$ CLS ensembles with $\mathcal O(a)$-improved Wilson fermions and Lüscher-Weisz gauge action. The set of ensembles covers a pion mass range of $M_\pi=130-353\,$MeV with lattice spacings between $a=0.05-0.09\,$fm. In particular, the ensemble list includes a $96^{3}$ box ensemble at the physical pion mass. For the purpose of the form factor extraction, we employ both the summed operator insertion method (summation method) and explicit two-state fits in order to account for excited-state contributions to the nucleon correlation functions. As for the description of the $Q^{2}$-behavior of the form factors, we perform $z$-expansion fits. Finally, we present HBChPT-inspired chiral and continuum extrapolations of the data.
Lattice techniques are the most reliable ones to investigate its phase diagram in the temperature-baryon density (chemical potential) plane. They are, however, well-known to be saddled with a variety of problems at nonzero density. I address here the old question of placing the baryonic (quark) chemical potential on the lattice and point out that important consequences for the current and future experimental searches of QCD critical point.
We present an update on our efforts to determine the QCD phase diagram using complex Langevin simulations. In this study, we use two flavours of Wilson fermions with moderate pion masses ($\sim 450$ MeV). To improve the convergence of the simulations, we employ adaptive step size scaling and dynamic stabilisation. Here we report on our findings at higher temperatures and density. In addition, we also report on the eigenvalue spectrum for increasing chemical potential and smaller temperatures.
All methods currently used to study finite baryon density lattice QCD suffer from uncontrolled systematic uncertainties in addition to the well-known sign problem. We formulate and test a method - sign reweighting - that works directly at finite chemical potential and is yet free from any such uncontrolled systematics: with this approach the only problem is the sign problem itself. In practice the approach involves the generation of configurations with the positive fermionic weights $\left| \rm{Re} \rm{det} D(\mu) \right|$ where $D(\mu)$ is the Dirac matrix and the signs $\rm{sign} \left( \rm{Re} \rm{det} D(\mu) \right) = \pm 1$ are handled by a discrete reweighting. Hence there are only two sectors, $+1$ and $−1$ and as long as the average $\left< \pm 1 \right> \neq 0$ (with respect to the positive weight) this discrete reweighting has no overlap problem - unlike other reweighting methods - and the results are reliable. We will also present results based on this algorithm on the phase diagram of lattice QCD with two different actions: as a first test, we apply the method to calculate the position of the critical endpoint with unimproved staggered fermions at $N_\tau=4$; as a second application, we study the phase diagram with 2stout improved staggered fermions at $N_\tau=6$. This second one is already a reasonably fine lattice - relevant for phenomenology.
In typical statistical mechanical systems the grand canonical partition function at finite volume is proportional to a polynomial of the fugacity $\exp(μ/T)$. The zero of this Lee-Yang polynomial closest to the origin determines the radius of convergence of the Taylor expansion of the pressure around $μ=0$. Rooted staggered fermions, with the usual definition of the rooted determinant, do not admit such a Lee-Yang polynomial. We show that the radius of convergence is then bounded by the spectral gap of the reduced matrix of the unrooted staggered operator. We suggest a new definition of the rooted staggered determinant at finite chemical potential that allows for a definition of a Lee-Yang polynomial. We perform a finite volume scaling study of the leading Lee-Yang zeros and estimate the radius of convergence extrapolated to infinite volume using stout improved staggered fermions on $N_t$=4 lattices. In the vicinity of the crossover temperature at zero chemical potential, the radius of convergence turns out to be at $μ_B/T$≈2 and roughly temperature independent.
The phase diagram and the location of the critical endpoint of lattice QCD was determined earlier with unimproved staggered fermions on a Nt=4 lattice with the multiparameter reweighting method by studying Fisher zeros. In our recent work, as an extension of the old analysis we introduced stout smearing in the fermion action in order to reduce the finite lattice spacing effects. In this talk we will show that increasing the smearing parameter ρ the crossover at μ=0 gets weaker, i.e., the leading Fisher zero gets farther away from the real axis. Furthermore as the chemical potential is increased the overlap problem gets severe sooner than in the unimproved case, therefore shrinking the range of applicability of the method. Nevertheless, even after introducing the smearing certain qualitative features remain, which will be discussed in this talk.
Deforming the domain of integration after complexification of the field variables is an intriguing idea to tackle the sign problem. In thimble regularization the domain of integration is deformed into an union of manifolds called Lefschetz thimbles. On each thimble the imaginary part of the action stays constant and the sign problem disappears. A long standing issue of this approach is how to determine the relative weight to assign to each thimble contribution in the (multi)-thimble decomposition. Yet this is an issue one has to face, as previous work has shown that different theories exist for which the contributions coming from thimbles other than the dominant one cannot be neglected. Historically, one of the first examples of such theories is the one-dimensional Thirring model.
Here we discuss how Taylor expansions can be used to by-pass the need for multi-thimble simulations. If multiple, disjoint regions can be found in the parameters space of the theory where only one thimble gives a relevant contribution, multiple Taylor expansions can be carried out in those regions to reach other regions by single thimble simulations. Better yet, these Taylor expansions can be bridged by Padé interpolants. Not only does this improve the convergence properties of the series, but it also gives access to information about the analytical structure of the observables. The true singularities of the observables can be recovered. We show that this program can be applied to the one-dimensional Thirring model and to a (simple) version of HDQCD. But the general idea behind our strategy can be helpful beyond thimble regularization itself, i.e. it could be valuable in studying the singularities of QCD in the complex $\hat{\mu}_B$ plane. Indeed this is a program that is currently being carried out by the Bielefeld-Parma collaboration.
A new approach is presented to explore the singularity structure of lattice QCD at imaginary chemical potential. Our method can be seen as a combination of the Taylor expansion and analytic continuation approaches. Its novelty lies in using rational (Padé) approximants for studying the analytic continuation. The motivation for using rational approximants will be exhibited. We will also try to provide some confidence in our approach based on numerical experiments performed on well-motivated "toy models". Our focus lies in identifying singularities of the net-baryon number density in the complex $\mu_B$ plane. To this end we have found signatures of the Roberge-Weiss critical point and Chiral singularities. In this talk we will discuss the setup, simulation parameters and results obtained for 2+1 QCD at different temperatures and imaginary chemical potential values.
Lee-Yang edge singularities have been studied in various spin models to
investigate the analytic structure of the ferromagnetic transition. As
part of the Bielefeld Parma collaboration we investigate Lee-Yang
singularities in lattice QCD. Based on an analytic continuation of the
net-baryon number density, we present results of the location of the
closest singularities in the complex chemical potential plane, obtained
with (2+1)-flavor of highly improved staggered quarks (HISQ) on lattices
with temporal extent of $N_{\tau}=4, 6$. We show that their temperature
scaling is in accordance with the expected scaling of the Lee-Yang edge
singularities in the vicinity of the Roberge-Weiss transition. The
analysis can be used to determine various non-universal parameters that
map QCD in the scaling region of the RW transition to the Ising model.
We will further discuss how the Lee-Yang edge singularity can be used to
probe also the chiral phase transition in QCD. At temperatures close to
the chiral phase transition temperature $T_c$ we find again agreement
with the expected scaling of the Lee-Yang edge singularity, now
expressed in terms of scaling variables that are appropriate for the
chiral symmetry breaking. Finally, we discuss the scaling of the
Lee-Yang edge singularity in the vicinity of a possible critical end
point in QCD, at even lower temperatures. In the future, such a scaling
analysis might hint on the existence and location of the critical end point.
Taylor expansion of the equation of state of QCD suffers from shortcomings at chemical potentials $\mu_B>(2−2.5) T$. First, one faces difficulties inherent in performing such an expansion with a limited number of coefficients; second,higher order coefficients determined from lattice calculations suffer from a poor signal-to-noise ratio.
We present a novel scheme for extrapolating the equation of state of QCD to finite, real chemical potential that can extend its reach further than previous methods.
We show continuum extrapolated lattice results for the new expansion coefficients and for the thermodynamic observables up to $\mu_B/T \simeq 3.5$.
Taylor expansion in powers of baryon chemical potential ($\mu_B$) is an oft-used method in lattice QCD to compute QCD thermodynamics for $\mu_B\ne0$. We introduce a new way of resumming the contribution of the first $N$ Taylor coefficients to the lattice QCD equation of state to all orders in $\mu_B$. The method reproduces the truncated Taylor expansion when re-expanded in powers of $\mu_B$. We apply the proposed approach to high-statistics lattice QCD calculations using 2+1 flavors of Highly Improved Staggered Quarks with physical quark masses on $32^3\times8$ lattices and for temperatures $T\approx145-175$ MeV. We demonstrate that our resummed version leads to a markedly improved convergence compared to the standard Taylor series approach. We also demonstrate the connection between our approach and reweighting. Lastly, our method runs into the Sign Problem which allows us to determine the maximum value of $\mu_B$ beyond which this method breaks down. We connect this maximum value of $\mu_B$ to the zeros of the partition function in the complex-$\mu_B$ plane.
The hadron resonance gas (HRG) model is often believed to correctly describe the confined phase of QCD. This assumption is the basis of many phenomenological works on QCD thermodynamics and of the analysis of hadron yields in relativistic heavy ion collisions. We use first-principle lattice simulations to calculate corrections to the ideal HRG. Namely, we determine the sub-leading fugacity expansion coefficients of the grand canonical free energy, receiving contributions from processes like kaon-kaon or baryon-baryon scattering. We achieve this goal by performing a two dimensional scan on the imaginary baryon number chemical potential ($\mu_B$) - strangeness chemical potential ($\mu_S$) plane, where the fugacity expansion coefficients become Fourier coefficients. We carry out a continuum limit estimation of these coefficients by performing lattice simulations with temporal extents of $N_\tau = 8, 10, 12$ using the 4stout-improved staggered action. We then use the truncated fugacity expansion to extrapolate ratios of baryon number and strangeness fluctuations and correlations to finite chemical potentials. Evaluating the fugacity expansion along the crossover line, we reproduce the trend seen in the experimental data on net-proton fluctuations by the STAR collaboration.
We present a novel method which enables a continuous temperature sampling in a single Monte-Carlo simulation.
The method can be generally used to compute continuous temperature dependence of any observable and we use it to evaluate the temperature dependence of QCD topological susceptibility at very high temperatures.
The various advantages and disadvantages of the method will be presented. Work based on Phys.Rev.D 104 (2021) 1, 014502.
The Fermilab experiment recently published their new measurement of the anomalous magnetic moment of the muon, confirming the Brookhaven's measurement with a comparable precision. Combining those two results and using the theory estimate published by the "Muon $g-2$ theory initiative", a discrepancy of about 4 sigmas is observed between experiment and the theory prediction based on the Standard Model of particle physics. However, some lattice QCD calculations tend to produce larger values for the hadronic vacuum polarisation compared to the data-driven approach, bringing the SM prediction closer to the experimental measurement.
In this talk, we present an update of the leading hadronic vacuum polarization contribution from the Mainz group using $N_f=2+1$ O($a$)-improved Wilson quarks. We will focus on the isoscalar channel for the $g-2$ contribution and on the window quantities that can be used as benchmarks between different lattice calculations.
The Euclidean time windows defined in RBC/UKQCD 2018 provide a means to test the consistency of different lattice results as well as the consistency with the data-driven R-ratio results on a short timescale. This is of particular urgency due to an apparent emerging tension between data-driven results and some lattice results. I will present an update to the 2018 RBC/UKQCD result for Euclidean time windows for the hadronic vacuum polarization (HVP) contribution to the muon g-2.
We present a lattice calculation of the Euclidean position-space windows contributing to the leading-order hadronic vacuum polarization term of the muon anomalous magnetic moment $a_\mu$.
Short-, intermediate- and long-distance windows are considered in order to isolate different scales sensitive to specific integration ranges of experimental time-like data used in the R-ratio.
By adopting the same smooth window function introduced by the RBC and UKQCD Collaborations with width parameter $\Delta = 0.15~\rm fm$, for the isospin-symmetric, light, quark-connected component we get $a_\mu^{\rm SD} (ud, \rm iso) = 48.21\,(80) \times 10^{-10}$ , $a_\mu^{\rm W} (ud, \rm iso) = 202.2\,(2.6) \times 10^{-10}$ and $a_\mu^{\rm LD} (ud, \rm iso) = 382.5\,(11.7) \times 10^{-10}$ in the short- (SD), intermediate- (W) and long-distance (LD) time regions, respectively, with $t_0 = 0.4~\rm fm$ and $t_1 = 1.0~\rm fm$.
Our results are obtained using the gauge configurations generated by the Extended Twisted Mass Collaboration with $N_f=2+1+1$ dynamical quarks, at three values of the lattice spacing varying from 0.089 to 0.062 fm, at several lattice volumes and with pion masses in the range $M_\pi \simeq 220 - 490~\rm MeV$.
The first results from the Fermilab E989 experiment have confirmed the long-standing tension between the experimental determination of the muon anomalous magnetic moment $a_\mu=(g_\mu-2)/2$ and its SM determination using the dispersive approach. In order to match the expected final precision from E989, the current uncertainty on ab initio determinations using lattice QCD must be decreased by a factor 5-15, a goal which is hampered by the signal-to-noise ratio problem of the electromagnetic current correlator. Multi-level Monte Carlo integration with fermions is a method which reduces the variance of correlators exponentially in the distance of the fields. Here we demonstrate that the variance reduction in a realistic two-level simulation with a pion mass of 270 MeV, linear size of 3 fm and lattice spacing around 0.065 fm is sufficient to compute the tail of the current correlator with the statistical accuracy required for the hadronic vacuum polarization contribution to $a_\mu$. An efficient estimator is also employed for computing the disconnected contribution.
The anomalous magnetic moment of the muon $a_{\mu}$ and the running of the electromagnetic coupling $\alpha$ play a fundamental role in beyond Standard Model (SM) physics searches. Non-perturbative hadronic contributions to both quantities, which are related to the hadronic vacuum polarization (HVP) function consisting of two electromagnetic currents, are a main source of uncertainty in the SM prediction. We compute the HVP function in lattice QCD+QED applying the time-momentum representation method. We expand the relevant correlation functions around the isosymmetric limit. In particular, we focus on leading isospin breaking effects taking connected contributions into account, which we evaluate on isosymmetric $N_{\mathrm{f}}=2+1$ QCD gauge ensembles generated by the CLS initiative with non-perturbatively $O(a)$-improved Wilson fermions.
Recently, the Budapest-Marseille-Wuppertal collaboration has achieved a sub-percent precision in the evaluation of the HVP contribution to the muon g-2. At this level of precision, pure isospin-symmetric QCD is not sufficient. In the talk we will review how QED and strong isospin breaking effects have been included in our work. Isospin-breaking is implemented by expanding the relevant correlation functions to second order in electric charge and to first order in $(m_d-m_u)$. The correction terms are then computed using isospin-symmetric configurations. The choice of this approach allows us to better distribute the available computing resources among the various contributions.
Transition form factors of light pseudoscalar mesons ($\pi^0$, $\eta$ and $\eta^{\prime}$) play a crucial role in computing the hadronic light-by-light contribution to the muon anomalous magnetic moment.
We present first results toward the extraction of these form factors using lattice QCD with staggered fermions on $N_f=2+1+1$ gauge ensembles of the Budapest-Marseille-Wuppertal collaboration. The first part of the talk will focus on the spectroscopy of the three mesons. In the second, we will expound on our strategy to extract the form factors.
We report on our computation of the pion transition form factor $\mathcal{F}_{\pi \rightarrow \gamma^* \gamma^*}$ from twisted mass lattice QCD, to determine the numerically dominant light pseudoscalar pole contribution for the analysis of hadronic light-by-light scattering in the muon $g-2$. The pion transition form factor is computed directly at the physical point. We present first results for our estimate of the pion pole contribution to $a_\mu$ with kinematic setup of the pion at rest at a single lattice spacing.
The tension between theory and experiment for the anomalous magnetic moment of the muon ($a_\mu$) is one of the long-standing puzzles of modern particle physics. After the update by the Fermilab E989 experiment in April 2021, the discrepancy between both sides lies at the 4.2-sigma level, as of the consensus made in the 2020 muon g-2 theory White Paper. The theory error is entirely dominated by the hadronic contributions, which can be calculated using lattice QCD. The order $\alpha_{\textrm{QED}}^3$ hadronic light-by-light (hlbl) contribution $a_\mu^{\textrm{hlbl}}$ admits a large relative uncertainty and represents a non-negligible source of uncertainty for the total error budget. In this talk, the Mainz approach and result for $a_\mu^{\textrm{hlbl}}$ computed with $N_f=2+1$ lattice ensembles [arXiv:2104.02632] will be presented. We obtain a value of $a_\mu^{\textrm{hlbl}}=106.8(14.7)\times 10^{-11}$ after a chiral, continuum and infinite-volume extrapolation. This result contains all five Wick-contraction topologies needed for a complete lattice determination of $a_\mu^{\textrm{hlbl}}$.
We propose a method to help control cutoff effects in the short-distance contribution to integrated correlation functions, such as the hadronic vacuum polarization, using the corresponding screening correlators computed at finite temperature. The strategy is investigated with Wilson fermions at leading order, which reveals a logarithmically-enhanced lattice artifact in the short-distance contribution, whose coefficient is determined at this order. We also perform a numerical study with $N_\mathrm{f}=2$ $\mathrm O(a)$-improved Wilson fermions and a temperature $T\approx 250~\mathrm{MeV}$, with lattice spacings down to $a=0.03~\mathrm{fm}$, which suggests good control can be achieved on the short distance contribution to the hadronic vacuum polarization and the Adler function at large virtuality. Finally, we put forward a scheme to compute the complete hadronic vacuum polarization function at large virtualities using a step-scaling in the temperature.
As present and future experiments in both the energy and precision frontiers look to identify new physics beyond the Standard Model, they require increasingly precise determinations of fundamental quantities like the electroweak couplings at various momenta. The latter can be obtained from experimental measurements or a particular reference value and the dependence on the energy. A precise, entirely theoretical determination of the running couplings is highly desirable, even more since the preliminary results of the E989 experiment in Fermilab were published, and non-perturbative techniques at small momentum are necessary.
In our talk, we present the latest results on these quantities of the Mainz group. We analyze a broad set of Coordinated Lattice Simulations ensembles with the time-momentum representation at various lattice spacings and pion masses. We perform an extrapolation to the physical point, we predict the running and compare it with other determinations, both from the lattice and phenomenology.
We investigate the impact of the latest Mainz/CLS collaboration's result for the hadronic vacuum polarization (HVP) on the electroweak (EW) precision tests. The subject is closely related to the muon g-2 via the HVP. Both precision tests come under scrutiny with respect to physics Beyond the Standard Model. Our HVP calculation is used for the running electromagnetic coupling at low energy and linked at various matching energies to the higher energy running evaluated by phenomenological approaches. We predict the electromagnetic coupling at the Z-pole (alpha(Mz)), providing a lattice-driven input to EW-global fits. Our evaluation of alpha(Mz) is stable for a wide range of matching energies and comes with various systematics taken into account. In light of our alpha(Mz) determination, we discuss a known tension in the EW-global fits.
Gauge theories admit a generalisation in which the gauge group is replaced by a finer algebraic structure, known as a 2-group. The first model of this type is a Topological Quantum Field Theory introduced by Yetter. I would like to discuss a common generalisation of both the Yetter’s model and Yang-Mills theory. I will focus on the lattice formulation of such model for finite 2-groups. After describing the model I will mention its integrable limits and state some basic expectations about its dynamics.
In this talk, I discuss a simple model based on the symmetry group $Z_2$ belonging to the class of 2-group gauge systems. Particular limits of such systems correspond to certain types of topological quantum field theories. In the selected model, independent degrees of freedom are associated to both links and faces of a four-dimensional lattice and are subject to a certain constraint. I present the details of this construction, discuss the expected dynamics in different regions of phase space and show numerical results from Monte Carlo simulations confirming these expectations.
The Thirring model describes relativistic fermions with a contact interaction between conserved fermion currents. In 2+1 spacetime dimensions its U($2N$) global symmetry is broken at strong coupling to U($N)\otimes$U($N$) through generation of a non-vanishing bilinear condensate $\langle\bar\psi\psi\rangle\not=0$. I present results of numerical simulations of the single-flavour model using domain wall fermions, which preserve U(2) in the limit wall separation $L_s\to\infty$. The results confirm symmetry breaking takes place implying the critical flavour number $N_c\geq1$. I will also present results for the critical equation of state showing it is consistent with the existence of a quantum critical point with critical exponents distinct from those obtained with staggered fermions.
Modelling the behaviour of strongly interacting fermion sytems with correct symmetry properties presents significant challenges for lattice field theories. Investigating the suitability of domain wall fermions, we explore the locality and the Ginsparg-Wilson error of the Dirac operator in the context of a dynamical 2+1D non-compact Thirring model. We further investigate the eigenvalues of the Dirac operators and the Banks-Casher relation, as part of a broader search for criticality. Relations between twisted mass domain wall and overlap formulations are reviewed.
The Hubbard model is an important tool to understand the electrical properties of various materials. More specifically, on the honeycomb lattice it features a quantum phase transition from a semimetal to a Mott insulating state which falls into the Gross-Neveu universality class. In this talk I am going to explain how we confirmed said quantum phase transition by taking advantage of recent improvements in our Hybrid Monte Carlo algorithm. These improvements allowed us to simulate unprecedentedly large lattices and extract critical quantities with very high precision.
Quantizing topological excitations beyond a semiclassical approximation is a nontrivial issue. Examples of relevant topological excitations are vortices in (2+1) dimensions. They are the condensed matter analogs of monopoles in particle physics and arise in Bose-Einstein condensates and superfluids. These systems can be described by the (2+1)-d O(2) model, where vortices are present through nontrivial winding of the field. This model can be dualized into scalar QED and, in the broken phase, the vortex becomes an infraparticle that is surrounded by a cloud of photons spreading out to infinity. As Gauss's law forbids a single charged particle to be placed in a periodic volume, it equivalently forbids a single vortex to exist by itself. We circumvent this issue, without breaking translation invariance, by imposing C-periodic boundary conditions. By simulating the dual theory, scalar QED, we compute the universal finite-volume vortex mass and charge near the Wilson-Fisher fixed point.
$\mathcal{N}=1$ SUSY Yang-Mills theory is an appealing theoretical framework that has been studied in the literature using different methods, including standard lattice simulations. Among these, the volume-reduced twisted Eguchi-Kawai model, endowed with one adjoint Majorana fermion, could play an important role in studying its large-$N$ limit via the Curci-Veneziano prescription. In this talk, we present our results on the analysis of the scale of the theory, performed via different methods based on purely gluonic observables as well as (quenched) fundamental mesons in the chiral limit. These lattice results will be used as a scale setting for the analysis of the spectrum of the theory.
We report on an ongoing study of the running coupling of SU(N) pure Yang-Mills theory in the twisted gradient flow scheme (TGF). The study exploits the idea that twisted boundary conditions reduce finite volume effects, leading to an effective size in the twisted plane that combines the number of colours and the torus period. We test this hypothesis by computing the TGF running coupling and the SU(N) Lambda parameter on asymmetric lattices of size $(N L)^2 × L^2$ for various gauge groups. Finite volume effects are monitored by analyzing the coupling in different planes and by comparing results at different number of colours.
We describe new theoretical opportunities arising from the possibility to solve the gradient flow (GF) equations taking into account the fermion determinant exactly employing non-iterative solvers. Using this exact GF we can find real saddle points of the lattice action at zero chemical potential and trace their evolution in complex space at non-zero chemical potential. We show that these saddle points correspond to modified instantons, where the back reaction from the fermion determinant is taken into account already at the level of the Euclidean field equations. We demonstrate how this approach leads to the rigorous numerical procedure for the definition of the inter-instanton interactions and give examples of interaction profiles computed in this way.
We show two possible applications of this technique. First of all, the knowledge of the saddle points can help us to simplify the structure of the Lefschetz thimbles decomposition and to alleviate the sign problem. The second application is the systematic building of a statistical model of interacting instantons from first principles without need of any phenomenological input.
We describe the systematic treatment of the gradient flow at higher orders in perturbation theory and its application within the small flow-time expansion. The results include the coefficients of the gradient-flow definition of the energy-momentum tensor, the quark and the gluon condensates, as well as the hadronic vacuum polarization at next-to-next-to-leading order in the strong coupling. Combined with suitable lattice calculations, these results allow for independent approaches to various phenomenological problems of low-energy QCD.
The 1-loop RG flows in the most general local, renormalizable, Euclidean, classically scale invariant and globally SU(N) invariant theory of vector fields is computed. The total number of dimensionless couplings is 7 and several asymptotically free RG flows are found which are not gauge theories but nonetheless perfectly well-defined Euclidean QFT's. The set of couplings is extended to 9 with the most general globally SU(N) invariant ghost couplings and Yang-Mills theory is shown to emerge on a particular RG flow. Several marginal gauge symmetry breaking deformations of Yang-Mills theory are also found.
The one-loop determination of the coefficient $c_{\text{SW}}$ of the Wilson quark
action has been useful, in conjunction with non-perturbative
determinations of $c_{\text{SW}}$, to push the leading cut-off effects for on-shell
quantities to $\mathcal{O}(\alpha^2 a)$, or eventually $\mathcal{O}(a^2)$, if no link-smearing is
employed. These days it is common practice to include some link-smearing
into the definition of the fermion action. Unfortunately, in this
situation only the tree-level value $c_{\text{SW}}^{(0)}=1$ is known, and
cut-off effects start at $\mathcal{O}(\alpha a)$. We present some general techniques
for calculating one loop quantities in lattice perturbation theory
which continue to be useful for smeared-link fermion actions.
Specifically, we discuss the application to the 1-loop improvement
coefficient $c_{\text{SW}}^{(1)}$ for stout-smeared Wilson fermions.
I will discuss the RBC & UKQCD collaboration's recent lattice calculation of $\epsilon'$, the measure of direct CP-violation in kaon decays. This result significantly improves on our previous 2015 calculation, with nearly 4x the statistics and more reliable systematic error estimates. I will also discuss how our results demonstrate the Standard Model origin of the $\Delta I=1/2$ rule, and will present our plans for future calculations.
The Cabibbo–Kobayashi–Maskawa (CKM) matrix element $|V_{ub}|$ describes the coupling between $u$ and $b$ quarks in the weak interaction, and is one of the fundamental parameters of the Standard Model. $|V_{ub}|$ is the focus of a longstanding puzzle, as the world-average values derived from inclusive and exclusive $B$-meson decays show a tension of a few standard deviations.
Semileptonic decays can be used to extract CKM elements by combining a lattice QCD calculation of the form factors and the experimental branching fractions. This talk will focus on the recent lattice QCD results and the current status of $V_{ub}$.
Exotic states have been predicted before and after the advent of QCD.
In the last decades they have been observed at accelerator experiments in the sector with two heavy quarks, at or above the quarkonium strong decay threshold and called X Y Z states.
These states offer a unique possibility for investigating the dynamical properties of strongly correlated systems in QCD.
I will show how an alliance of nonrelativistic effective field theories and lattice can allow us to address these states in QCD. In particular I will explain what are the opportunities and challenges of lattice QCD in this respect and which new tools should be developed.
This talk will offer an overview of the role of lattice field theory in strongly interacting BSM phenomenology.
I discuss progress in simulating field theories on discrete hyperbolic spaces, with the goal of studying their physics in the bulk, and on the boundary. At tree-level, a free scalar field propagating in the bulk lattice is found to possess power-law two-point correlation functions on the boundary. The power-law behavior excellently matches the expected Klebanov-Witten formula despite being far away from the continuum, as well as matching the expected form due to the explicit breaking of conformal symmetry from the finite-volume boundary. When the field is dynamical---in the case of Ising spins---on a fixed hyperbolic lattice, the boundary physics is separated into two regimes depending on the bulk nearest-neighbor coupling. The conformal behavior of the free field---as well as the strong-coupling limit of the dynamical field---on the boundary can be seen explicitly to be a consequence of the hyperbolic geometry.
Physics colloquium-level lecture on QCD, webcast publicly
Title: QCD: The Glory and The Power
Abstract: After a brief oration in praise of the ideal mathematical beauty of QCD and its imposing experimental success, I will describe several of its ongoing and future applications at the frontiers of knowledge. These are the frontier of precision (muon $g-2$), the frontier of high temperature and density (heavy ion collisions), the frontier of late stellar evolution (supernovae and neutron stars), and the frontier of theoretical adventure (axions and dark matter).
We develop a gauge covariant neural network for four dimensional non-abelian gauge theory, which realizes a map between rank-2 tensor valued vector fields. We also find the conventional smearing procedures for gauge fields can be regarded as this neural network with fixed parameters. We developed a formula to train the network as an extension of the delta rule, which is used in machine learning context. In addition, we perform simulation with self-learning hybrid Monte-Carlo (SLHMC) in 4 dimension for SU(N) with dynamical fermions as a demonstration of the network and the training formula. SLHMC, which is an exact algorithm, uses parametrized force in the molecular dynamics step, and we employed neural network parametrized action and we obtained consistent results with HMC. This talk is based on arXiv:2103.11965 and some additional materials.
Highly oscillatory path integrals are common in lattice field theory. They crop up as sign problems and as signal to noise problems and prevent Monte Carlo calculations of both lattice QCD at finite chemical potential and real-time dynamics. A general method for treating highly oscillatory path integrals has emerged in which the domain of integration of the path integral is deformed into a complexified field space. In this talk I will review this method, and I will discuss recent progress in machine learning manifolds for lattice QCD.
Complex contour deformations of the path integral have previously been shown to mitigate extensive sign problems associated with non-zero chemical potential and real-time evolution in lattice field theories. This talk details recent extensions of this method to observables affected by signal-to-noise problems in theories with real actions. Contour deformations are shown to result in redefinitions of observables which do not affect their expectation value and do not modify the Monte Carlo sampling weights. The choice of contour does, however, affect the variance and can be optimized to maximize the signal-to-noise ratio. Families of contour deformations are defined for SU(N) variables and optimized deformations are shown to give exponential improvements in the signal-to-noise ratio of Wilson loops in proof-of-principle applications to U(1) and SU(N) lattice gauge theories.
In this work, we obtained the finite temperature Bottomonium interaction potential from the first principle lattice-NRQCD calculation of Bottomonium mass and width [Phys.Lett.B 800, 135119 (2020)]. We find that the HTL complex potential is disfavored by the lattice result, which motives us to employ a model-independent parameterization --- the Deep Neural Network (DNN) --- to represent the Bottomonium potential, extract the potential allowed by the lattice data.
The DNN is a widely used deep-learning method and can be treated as a model-independent parameterization to approximate arbitrary functional relations. In this work, we employ the DNN to represent the temperature-dependent Bottomonium potential and extract both the real and imaginary parts, $V_R(T,r)$ and $V_I(T,r)$. We find that while $V_I(T,r)$ increase with both temperature and distance, the extracted value is significantly greater than the HTL prediction. Also, while the color-screening effect is observed in $V_R(T,r)$, the temperature dependence is qualitatively weaker than other model calculations. Combined with the lattice result, our study suggests a new picture of Bottomonium dissociation. High excitation of bound states, such as 2P and 3S states, are allowed to exist at a temperature as high as $\sim0.33~$GeV. Their suppression in the Quark-Gluon Plasma is caused by the temperature-dependent decay width. The latter can be as high as $\sim 0.6$~GeV, which corresponds to the lifetime $\sim0.3$~fm. Such a new dissociation picture can be tested in precise comparison with Bottomonium observables in heavy-ion collisions.
Statistical modeling plays a key role in lattice field theory calculations. Examples including extracting masses from correlation functions or taking the chiral-continuum limit of a matrix element. We discuss the method of model averaging, a way to account for uncertainty due to model variations, from the perspective of Bayesian statistics. Statistical formulas are derived for model-averaged expectation values and for estimating the required model probability weights. In addition, we reframe the common problem of data subset selection (e.g. choice of minimum time separation for fitting a two-point correlation function) as a model selection problem and study model averaging as a universal alternative to hand tuning of fit ranges.
The lattice formulation of finite-temperature field theory is readily extended,
via the Schwinger-Keldysh contour, to accomodate the definition of real-time
observables. Unfortunately, this extension also induces a maximally severe sign
problem, obstructing the computation of, for example, the shear viscosity. In
the large-N limit of certain field theories, including $O(N)$-symmetric scalar
fields, observables can be computed via a saddle point expansion (closely
connected to the Lefschetz thimble programme for alleviating the fermion sign
problem). This expansion continues to work for real-time observables. In this
talk we present lattice calculations of real-time dynamics in scalar field
theory at large N, both near equilibrium (transport coefficients) and far from
equilibrium.
Reduced staggered fermions afford a very economical lattice fermion formulation yielding just two Dirac fermions in the continuum limit. They have also been used to construct models capable of symmetric mass generation. However, generically they suffer from sign problems. We discuss an application of the tensor renormalization group, a sign problem free method, to such models. We make a comparison between tensor renormalization group results and RHMC results in smaller volumes and show behaviors of physical observables in the thermodynamic and the continuum limits.
We present results of tensor network simulations of the three-dimensional O(2) model at nonzero chemical potential and temperature, which were computed using the higher order tensor renormalization group method. This also includes some enhancements to the method which take care of anisotropic tensors. Some special care was also taken to reduce the systematic error on the computation of the observables.
We present continuum limit results of the quark mass dependence of octet and decuplet baryon masses obtained from Lattice QCD simulations. This is part of our large-scale programme connected to CLS of simulating $N_f=2+1$ flavours of non-perturbatively improved Wilson fermions where ensembles with large volumes together with a wide range of quark masses, including the physical point, are used. The six different lattice spacings reach from 0.1 fm down to below 0.04 fm. In this analysis we also determine the Wilson flow scale parameter $t_0$ from the masses of the $\Xi$ and $\Omega$ baryons.
In this talk I will discuss several new results from the NPLQCD Collaboration that combine lattice QCD results on (hyper)nuclear systems at unphysical pion masses together with nuclear effective field theories. Two-baryon channels with strangeness $0$ to $-4$ are analized, with findings that point to interesting symmetries observed in hypernuclear forces as predicted in the limit of QCD with a large number of colors. Also, several matrix elements of light nuclei are studied. The tritium axial charge, related to the Gamow-Teller matrix element, and the longitudinal momentum fraction of ${}^3\text{He}$ that is carried by the isovector combination of $u$ and $d$ are extracted and extrapolated to the physical point. For this latter case, it can be seen how including lattice results to experimental determinations can have imminent potential to enable more precise determinations and to reveal the QCD origins of the EMC effect.
A calculation of baryon-baryon scattering via finite-volume spectroscopy using distillation will be reported. Ensembles with SU(3) flavor symmetry and a pion/kaon/eta mass of roughly 420 MeV, covering a wide range of lattice spacings, are employed. For the first time, we take the continuum limit, finding large discretization effects. In the singlet sector, we obtain a weakly bound H dibaryon.
We present the current status of our ongoing efforts in search of the H-dibaryon on $N_f=2+1$ CLS ensembles away from the SU(3) flavor symmetric point. Utilizing the distillation framework (also known as LapH) in its exact and stochastic forms, we calculate two-point correlation matrices using large bases of bi-local two-baryon interpolators to reliably determine the low energy spectra. We report the low lying spectrum on several relevant lattice irreducible representations for multiple ensembles with different lattice spacing and physical volumes. The status of finite volume analysis to extract the scattering amplitudes will also be discussed.
Multi-baryon systems are challenging to study with lattice QCD in particular because of small gaps between the ground state and excited states for large lattice volumes. Variational methods have long been known to be useful for disentangling closely spaced energy levels but require approximations to all-to-all quark propagators that are computationally prohibitive to compute exactly. In this talk, I will discuss a new method for computing multi-nucleon correlation-function matrices using sparsened all-to-all quark propagators and results for a variational calculation of the two-nucleon spectrum at mpi ~ 800 MeV using a large interpolating operator set including local hexaquark operators, nonlocal two-nucleon operators with plane-wave wavefunctions, and exponentially localized two-nucleon operators.
Lattice QCD calculations of two-nucleon interactions have been underway for about a decade, but still haven't reached the pion mass regime necessary for matching onto effective field theories and extrapolating to the physical point. Furthermore, results from different methods, including the use of the Luscher formalism with different types of operators, as well as the HALQCD potential method, do not agree even qualitatively at very heavy pion mass. In this talk I will discuss these issues and present steps toward an understanding of the various systematics at play.
The relationship between finite volume multi-hadron energy levels and matrix elements and two particle scattering phase shifts and decays is well known, but the inclusion of long range interactions such as QED is non-trivial. Inclusion of QED is an important systematic error correction to K->\pi\pi decays. In this talk, we present a method of including a truncated, finite-range Coulomb interaction in a finite-volume lattice QCD calculation. We show how the omission caused by the truncation can be restored by an infinite-volume analytic calculation so that the final result contains no power-law finite-volume errors beyond those usually present in Luscher’s finite-volume phase shift determination. This approach allows us to calculate the QED-corrected infinite-volume phase shift for \pi\pi scattering in Coulomb gauge, a necessary ingredient to K->\pi\pi, while neglecting the transverse radiation for now.
L\"{u} scher method for two-particle scattering is a critical tool for
connecting finite-volume spectrum to infinite-volume scattering phaseshifts.
We numerically validate the quantization conditions up to partial waves l=4.
Various setups used in practice are considered: cubic or elongated lattices, rest or moving frames, unequal or equal masses, and integer or half-integer total angular momentum.
We studied the decay rate of the particle decay $B^0 \rightarrow D^- \ell^+ \nu_{\ell}$ using data collected from the Belle Collaboration. In order to analyze this decay rate, we used three parameterizations of the form factor which describes this process, the CLN (Caprini, Lellouch, and Neubert) parametrization, the BGL (Boyd, Grinstein, and Lebed) parametrization, and the BCL (Bourrely, Caprini, and Lellouch) parameterization. This form factor is a function of the hadronic recoil variable $w$ and each parameterization contains unique free parameters which are the interest of this project. One of the goals of this project was to fit these different parameterizations of the form factor to the Belle data in the lattice regime, considering the data points where $w <$ $\sim 1.3$, so that we can predict what the larger $w$ region should look like. We hope to in the future be able to use Monte Carlo simulations to extract values of the form factors, however these simulations are only able to reliably extract these values inside of the lattice regime. By fitting only the low $w$ values, we are able to get an idea of what the larger $w$ region should look like and how many data points are needed in the fit to accurately predict the larger $w$ region.
In this talk, I will report our group's progress on calculating the nucleon axial form factor with the HISQ action for both valence and sea quarks. Nucleon matrix elements with staggered fermions require careful analysis of the staggered symmetry group. I will report a solution based on the generalized Wigner-Eckart theorem that enables us to extract physical observables from staggered observables. I will present published results for nucleon axial and vector charges and preliminary results on the form factors to demonstrate the feasibility of our methodology.
The Deep Underground Neutrino Experiment (DUNE) is an upcoming neutrino oscillation experiment that is poised to answer key questions about the nature of the neutrino. Lattice QCD has the ability to make significant impact upon DUNE by computing the interaction of a nucleon to a weak current. Nucleon amplitudes involving the axial form factor are part of the primary signal measurement process for DUNE, and precise calculations from LQCD can significantly reduce the uncertainty for inputs into Monte Carlo generators. Recent calculations of the nucleon axial charge have demonstrated that sub-percent precision is possible on this vital quantity. In this talk, I will discuss preliminary results for the Callat collaboration's calculation of the axial form factor of the nucleon. These computations are performed with M\"obius domain wall valence quarks on HISQ sea quark ensembles generated by the MILC and Callat collaborations. The results use a variety of ensembles including several at physical pion mass.
The tension between the lattice calculation, the experimental data and the PCAC relation of the nucleon axial form factors - axial and (induced)-pseudoscalar - has been understood as a systematic resulting from missing multihadron (nucleon and pions) excited states in the analysis. These low-lying excited states are hard to resolve in the conventional analysis. Fits to the temporal component of axial current (A4), with a large excited-state contamination, demonstrate the need for the low-lying excited state, and the resulting axial form factor satisfy the PCAC relation. We will present a full reanalysis of the axial form factors that incorporates the low-energy states. Extensions of this data-driven approach successful for the axial form factor analysis is also applied to the electromagnetic form factors. Continuum results for the nucleon charges and electromagnetic form factors will also be presented. These lattice calculations are performed with Clover valence quarks on the MILC 2+1+1-flavor HISQ ensembles.
The light-cone definition of Parton Distribution Functions (PDFs) does not allow for a direct ab initio determination employing methods of Lattice QCD simulations that naturally take place in Euclidean spacetime. In this presentation we focus on pseudo-PDFs where the starting point is the equal time hadronic matrix element with the quark and anti-quark fields separated by a finite distance. We focus on Ioffe-time distributions, which are functions of the Ioffe-time ν, and can be understood as the Fourier transforms of parton distribution functions with respect to the momentum fraction variable $x$. We present lattice results for the case of the nucleon addressing the physical point and continuum extrapolations. We also incorporate our lattice data in the NNPDF framework treating them on the same footing as experimental data and discuss in detail the different sources of systematics in the determination of the non-singlet PDFs.
Parton degrees of freedom (PDF) are classified in the Euclidean path-integral formulation of the hadronic tensor in QCD. They include the valence and connected sea partons, the connected sea antipartons, and the disconnected sea partons and antiprotons. These degrees of freedom are shown to be the same as those from the quasi-PDF, pseudo-PDF and lattice cross section approaches on the lattice.
It is advocated that the connected sea and the disconnected sea should be separated in the global analysis of the PDFs. This allows a direct comparison of moments of PDF with the individual lattice matrix elements for the u, d, and s partons in the connected and disconnected insertions respectively.
In view of the above classification in QCD, the separation of the connected and disconnected sea partons is accommodated with the CT18 parametrization of the global analysis of the parton distribution functions (PDFs). This is achieved with the help of the distinct small x behaviors of these two sea partons and the constraint from the lattice calculation of the ratio of the strange momentum fraction to that of the $\bar u$ or $\bar d$ in the disconnected insertion.
We present an ab initio calculation of the individual up, down, and strange quark unpolarized, helicity, and transversity parton distribution functions for the proton. The calculation is performed within the twisted mass clover-improved fermion formulation of lattice QCD. We use a $N_f = 2 + 1 + 1$ gauge ensemble simulated with pion mass $M_\pi = 250$ MeV, $M_\pi L \approx 3.8$ and lattice spacing $a = 0.0938$ fm. Momentum smearing is employed in order to improve the signal-to-noise ratio, allowing for the computation of the matrix elements up to nucleon boost momentum $P_3 = 1.24$ GeV. The lattice matrix elements are non-perturbatively renormalized and the final results are presented in the $\overline{\rm MS}$ scheme at a scale of 2 GeV.
We present a calculation of lattice QCD non-local matrix elements that can be used to determine polarized gluon Ioffe-time distribution and the corresponding parton distribution function using QCD short distance factorization. We construct the nucleon interpolation fields using the distillation technique and flow the gauge fields using the gradient flow. Our calculation is performed on a $32^3 \times 64$ isotropic lattice with a pion mass of 358 MeV.
Two-color QCD (QC$_2$D) with two flavors of staggered fermions is studied at imaginary and real quark chemical potential $\mu_q$ and $T>T_c$. Various methods of analytic continuation of the quark number density from imaginary to real quark chemical potentials $\mu_q$ are considered on the basis of the numerical results for imaginary $\mu_q$. At $T < T_{RW} $ we find that the cluster expansion model provides rather good analytic continuation. Its relation to the canonical formalism is discussed. At $ T > T_{RW}$ we see that the analytic continuation to the real values of $\mu_q$ based on trigonometric functions works equally well with the conventional method based on the Taylor expansion in powers of $\mu_q$.
We investigate the thermal QCD phase transition and its scaling properties on the lattice.
The simulations are performed with N_f=2+1+1 Wilson twisted mass fermions at
pion masses from physical up to heavy quark regime. We introduce a new chiral order parameter,
which is free from linear mass contributions and turns out to be useful for
the study of scaling behaviour. Our results are compatible with O(4) universal scaling for the physical pion mass and the temperature range [120:300] MeV. Violations to scaling at larger masses and other possible scenarios, including mean field behaviour and Z(2) universality class are also discussed.
We provide an estimation for the critical temperature in the chiral limit T_0.
Quenched QCD at zero baryonic chemical potential undergoes a
deconfinement phase transition at a critical temperature $T_c$, which is
related to the spontaneous breaking of the global center symmetry.
Including heavy but dynamical quarks breaks the center symmetry
explicitly and weakens the first order phase transition. For
decreasing quark masses the first order phase transition turns
into a smooth crossover at a critical $Z_2$ point. The critical quark
mass corresponding to this point has been examined with $N_f=2$ Wilson
fermions for several $N_\tau$ in a recent study within our group. For
comparison, we also localize the critical $Z_2$ point with $N_f=2$
staggered fermions on $N_\tau=8$ lattices. For this purpose we perform
Monte Carlo simulations for several quark mass values and various aspect
ratios in order to extrapolate to the thermodynamic limit. The critical
mass is obtained by fitting to a finite size scaling formula of the
kurtosis of the Polyakov loop. Our results indicate large cutoff
effects, requiring simulations on lattices with $N_\tau>8$.
We report on an onging study on the interplay between Roberge-Weiss(RW) and chiral transition in simulations of (2+1)-flavor QCD with an imaginary chemical potential. We established that the RW endpoint belongs to the Z(2) universality class when calculations are done with the Highly Improved Staggered Quark (HISQ) action in the Roberge-Weiss plane with physical quark masses. We also have explored a range of quark masses corresponding to pion mass values, $m_{\pi}\geq 40$ MeV and found that the transition is consistent with Z(2) universality class. We argue that observables, that were usually used to determine the chiral phase transition temperature, e.g. the chiral condensate and chiral susceptibility, are sensitive to the RW transition and are energy like observables for the Z(2) transition, contrary to the magnetic (oder parameter) like behavior at vanishing chemical potential. Moreover the calculations performed at $m_{\pi} \sim 40$ MeV also put an upper bound for a critical pion mass at zero chemical potential for a possible $1st$ order chiral phase transition. We furthermore determine the curvature of the pseudo-critical line close to the RW point and compare it with that at vanishing chemical potential.
In this talk, we discuss results for the Roberge Weiss (RW) phase transition at nonzero imaginary baryon and isospin chemical potentials, in the plane of temperature and quark masses. Our study focuses on the light tricritical endpoint which has already been used as a starting point for extrapolations aiming at the chiral limit at vanishing chemical potentials. In particular, we are interested in determining how imaginary isospin chemical potential shifts the tricritical mass with respect to earlier studies at zero imaginary isospin chemical potential. A positive shift might allow one to perform the chiral extrapolations from larger quark mass values, therefore making them less computationally expensive. We also present results for the dynamics of Polyakov loop clusters across the RW phase transition.
We study the thermodynamic properties of QCD at nonzero isospin chemical potential using improved staggered quarks at physical quark masses. In particular, we will discuss the determination of the equation of state at zero and nonzero temperatures and show results towards the continuum limit. Based on the results for the isospin density $n_I$, the phase diagram in the $(n_I,T)$-plane will also be discussed.
According to perturbation theory predictions, QCD matter in the zero-temperature, high-density limits of QCD at nonzero isospin chemical potential is expected to be in a superfluid Bardeen-Cooper-Schrieffer (BCS) phase of $u$ and $\bar{d}$ Cooper pairs. It is also expected, on symmetry grounds, that such phase connects via an analytical crossover to the phase with Bose-Einstein condensation (BEC) of charged pions at $\mu_I\ge m_\pi/2$.
With lattice results, showing some indications that the deconfinement crossover also smoothly penetrates the BEC phase, the conjecture was made that the former connects continuously to the BEC-BCS crossover.
We compute the spectrum of the Dirac operator, and use generalized Banks-Casher relations, to test this conjecture and identify signatures of the superfluid BCS phase.
We study QCD at finite temperature in the presence of imaginary electric fields. In particular, we determine the electric susceptibility, the leading coefficient in the expansion of the QCD pressure in the imaginary field. Unlike for magnetic fields, at nonzero temperature this coefficient requires a non-trivial separation of genuine electric field-related effects and spurious effects related to the chemical potential, which becomes an unphysical gauge parameter in this setting. Our results are based on lattice simulations with stout improved dynamical staggered quarks at several lattice spacings and volumes.
In this talk I examine the algorithmic problem of minimal coupling gauge fields of the Yang--Mills type to Quantum Gravity in the approach known as Causal Dynamical Triangulations (CDT) as a step towards studying, ultimately, systems of gravity coupled with bosonic and fermionic matter. I first describe the algorithm for general dimensions and gauge groups and then focus on the results obtained from simulations of 2d CDT coupled to Yang--Mills fields with U(1) and SU(2) gauge groups, where we studied both observables related to gravity and gauge fields, and compared them with analogous simulations in the static flat case.
Quantizing gravity is one big problem of theoretical physics and it's well-known that general relativity is not renormalizable perturbatively. Yet studies of quantum gravity on lattice have given evidence of the asymptotic safety scenario in which there is a strongly coupled UV fixed point. In this talk, I will talk about our study of the interaction of two scalar particles propagating on Euclidean dynamical triangulations working in the quenched approximation, which involves calculating the binding energy of a two-particle bound state. After taking the infinite-volume, continuum limit of the lattice calculation, our result is compatible with what is expected for the ground state energy by solving the Schrodinger equation for Newton's potential, providing further evidence for EDT as a theory of gravity in four dimensions. I will also show how we can determine the lattice spacing of EDT calculation for the first time.
After a brief introduction of Euclidean dynamical triangulations (EDT) as a lattice approach to quantum gravity, I will discuss the emergence of de Sitter space in EDT. Working within the semi-classical approximation, it is possible to relate the lattice parameters entering the simulations to the partition function of Euclidean quantum gravity. This allows to verify that the EDT geometries behave semi-classically, and by making contact with the Hawking-Moss instanton solution for the Euclidean partition function, I discuss how to extract a value of the renormalized Newton's constant from the simulations. This value is consistent with that of previous determination coming from the interaction of scalar particles. That the same universal constant appears in these two different sectors of the theory is a strong indication that EDT provides a viable formulation of quantum gravity.
Recent work in Euclidean dynamical triangulations (EDT) has provided compelling evidence for its viability as a formulation of quantum gravity. In particular the lattice value of the renormalized Newton's constant has been obtained by two distinct methods (the binding energy of scalar particles on the lattice, and comparison with the Hawking-Moss instanton). That these calculations yield mutually compatible results is a nontrivial check which indicates that the low-energy effective action of EDT does include the expected Einstein-Hilbert term, and the lattice value of Newton's constant fixes the coefficient of this term in lattice units. To make further contact with the low-energy theory we turn to the two-point function of the scalar curvature, which can be calculated both on the lattice and in the effective theory and which depends straightforwardly on the parameters of the latter. To compare with the lattice predictions we must perform a nontrivial one-loop calculation in the effective theory, which I will discuss in this talk.
We present a new method to numerically investigate the gravitational collapse of a free, massless scalar quantum field in the semiclassical approximation from a spherically symmetric, coherent initial state. Numerical results are presented for a small ($r_s=3.5 l_p$) wave packet in the l=0 approximation. We observe evidence for the formation of a horizon and study various systematic effects such as finite volume, time and radial discretization, different waveforms and vacuum subtraction procedures. Within our approximation, we find that the onset of the horizon formation is accelerated by semiclassical effects. Prospects for including higher angular momentum states and observing Hawking radiation are discussed.
If and how gauge theories thermalize is an unanswered question. Partly, this is due to the inability of lattice gauge theory (LGT) simulations to simulate out-of-equilibrium quantum dynamics on classical computers, but also due the difficulty of defining entanglement entropy in lattice gauge theories and finding schemes for its practical computation.
In this work, we study real-time thermalization dynamics of a $Z_2$ LGT in 2+1d using exact diagonalization. We develop a dual formulation for the reduced density operator, which allows us to compute the Entanglement Spectrum (ES) during the time evolution. We show that, in the regime where the system has topological order, it agrees with the low-energy effective Hamiltonian that describes the system in the presence of an open boundary. This finding is analogous to Li & Haldane's conjecture about the ES of fractional quantum Hall states, which we extend here to lattice gauge theories. Studying quench dynamics, we then extract the entanglement Hamiltonian of non-equilibrium states during time evolution using a variational scheme.
Our formulation can be generalized to more complicated Abelian and non-Abelian lattice gauge theories and may allow future quantum digital computers and analog quantum simulators to uncover the thermalization dynamics e.g. of Quantum Chromodynamics from first principles.
We compute a real-time inclusive scattering processes from the spectral function of a Euclidean two-point correlation function in the two-dimensional O(3) model. The intractable inverse problem is overcome using a recently-proposed algorithm to compute the desired spectral function smeared with a variety of finite-width kernels. Systematic errors due to finite volume, continuum limit, and spectral reconstruction are demonstrably controlled, enabling a determination of the smeared spectral functions at energies exceeding the four-particle production threshold. These results are in agreement with the known exact spectral function smeared with the corresponding kernels. Finally, the unsmeared spectral function is computed by extrapolation of the numerical data to the zero-smearing-width limit. Everything discussed here is (in principle) applicable in QCD to determine similar inclusive rates such as the R-ratio.
In non-Hermitian random matrix theory there are three universality classes for local spectral correlations: the Ginibre class and the nonstandard classes AI$^\dagger$ and AII$^\dagger$. We show that the continuum Dirac operator in two-color QCD coupled to a chiral U(1) gauge field or an imaginary chiral chemical potential falls in class AI$^\dagger$ (AII$^\dagger$) for fermions in pseudoreal (real) representations of SU(2). We introduce the corresponding chiral random matrix theories and verify our predictions in lattice simulations with staggered fermions, for which the correspondence between representation and universality class is reversed. Specifically, we compute the complex eigenvalue spacing ratios introduced recently. We also derive novel spectral sum rules.
We discuss developments in calculating multi-hadron form-factors and transition processes via lattice QCD. Our primary tools are finite-volume scaling relations, which map spectra and matrix elements to the corresponding multi-hadron infinite-volume amplitudes. We focus on two hadron processes probed by an external current, and provide various checks on the finite-volume formalism in the limiting cases of perturbative interactions and systems forming a bound state. By studying model-independent properties of the infinite-volume amplitudes, we are able to rigorously define form-factors of resonances.
We summarize the results of the recent work of calculating the $\pi\pi$ scattering phase shifts for both the s-wave I=0 and I=2 channels at 4 different energies around the kaon mass with physical quark mass and focus on three new topics presented in that work. (i) A determinant test that can be applied to multi-operator data at a single time separation to detect excited state contamination. (ii) A fitting strategy that exploits theoretical input to estimate the excited state error which improves upon the method used to estimate this error in our 2015 calculation. (iii) A method of presenting the combined error on a scattering phase shift determined from finite-volume studies, giving a phase shift error at fixed energy rather than errors on both the phase shift and the energy at which it is evaluated.
A variety of phenomena in the Standard Model and its extensions manifest in long-range processes involving on-shell multi-hadron intermediate states. Given recent algorithmic and conceptual progress, such processes are now realistic targets for lattice QCD. In this talk, I present a recently developed formalism that makes possible the determination of reactions of the form $1+\mathcal{J}\to2\to 1+\mathcal{J}$ from 2-, 3-, and 4-point functions in a finite-volume Euclidean spacetime. I also give an outlook for the study of more complicated reactions.
There are a number of tetraquark channels for which some phenomenological models -- already constrained by the ordinary meson and baryon spectrum -- predict deep binding. We present results from our lattice calculations of doubly-charmed and bottom-charm channels where such predictions exist. Finding no evidence of deep binding, we can rule out those models, although this does not preclude the possibility of shallow binding for those states. On the other hand, a consistent picture of deeply-bound, strong-interaction stable $I=0$, $J^P=1^+$ $ud\bar{b} \bar{b}$ and $I=1/2$, $J^P=1^+$ $\ell s \bar{b}\bar{b}$ (with $\ell=u/d$) tetraquarks has emerged from lattice studies over the last few years. We discuss the current status of our calculations in each channel, outlining improvements that place our results on a firmer quantitative footing. The resulting updated versions of our earlier results for the binding energies of the two doubly-bottom channels are also presented.
We present the first calculation within lattice QCD of excited light meson resonances with $J^{PC} = 1^{--}$, $2^{--}$ and $3^{--}$. Working with an exact SU(3) flavor symmetry, for the singlet representation of pseudoscalar-vector scattering, we find two $1^{--}$ resonances, a lighter broad state and a heavier narrow state, a broad $2^{--}$ resonance decaying in both $P$-- and $F$--waves, and a narrow $3^{--}$ state. We present connections to experimental $\omega^\star_J, \phi^\star_J$ resonances decaying into $\pi \rho$, $K\bar{K}^*$, $\eta \omega$ and other final states.
based upon material appearing in
arXiv:2012.00518
C.T. Johnson, and J.J. Dudek
for the Hadron Spectrum Collaboration
The two-photon decay process ηc→2γ can provide an ideal testing ground for the understanding of nonperturbative nature of QCD. In this study, we propose a direct method to calculate the matrix element of a hadron decaying to two-photon. Various systematic effects are examined in this work. The method developed here can also be applied for other processes which involve the leptonic or radiative particles in the final states.
WE perform an exploratory study of glueballs on a RBC/UKQCD gauge ensembles with a large
lattice size and with the $N_f = 2 + 1$ dynamical quark masses being tuned at the physical point. The
noises of glueball correlation functions are considerably reduced through the cluster-decomposition-
error-reduction scheme. The Bethe-Salpeter wave functions are obtained for the salar, the tensor
and the pseudoscalar glueballs by using the spatially extended glueball operators defined through
the gauge potential $A_\mu(x)$ in the Coulomb gauge. These wave functions show similar features of
non-relativistic two-gluon systems, which are used to optimize the signals of the related correlation
functions at the early time region, where the ground state masses in each channel can be extracted.
By the assumptions that the glueball operators defined in terms gauge potentials couple almost
exclusively to pure glueball states, the obtained masses are interpreted to be those of the ground
state pure gauge glueballs. For the most interesting scalar channel, the glueball mass is determined
to be 1.75(2) GeV, which is in good agreement with the QLQCD predictions and is close to the
mass of $f_0 (1710)$. Our result shows the existence of glueball states in the presence of dynamical
quarks, even though many systematic uncertainties have not yet be well tackled with.
Removing ultraviolet noise from the gauge fields is necessary for glueball spectroscopy in lattice QCD. It is known that the Yang-Mills gradient flow method is an alternative approach instead of smearing or fuzzing of the links in various aspects. In this talk, we study the application of the gradient flow technique to the construction of the extended glueball operators. We find that a simple application of the original gradient flow method has some problems in glueball mass calculations at large flow time. To avoid this problem, only the spatial links are evolved by the ``spatial gradient flow'', which is defined by the spatial gradient of the Wilson plaquette action. We examine the new gradient flow approach in calculations of glueball two-point functions and Wilson loops, and then discuss its efficiency in comparison with the original gradient flow method and traditional smearing methods.
We present our calculation of the unpolarized gluon parton distribution function (PDF) in the nucleon using the Pseudo-PDF technique on a $32^3 \times 64$ isotropic lattice with a pion mass of 358 MeV. The nucleon interpolating fields are reconstructed using distillation and we apply the sGEVP method to calculate the gluonic matrix elements. We smear the gauge fields using the gradient-flow to compute the flowed matrix elements and using the double ratio, we calculate the flowed reduced Ioffe-time distribution (rITD). We extrapolate the results to the flow-time independent rITD and calculate the light-cone ITD in the $\overline{MS}$ scheme, at the small z-separation limit, using an NLO matching formula. Finally, the gluon PDF is calculated from the light-cone ITD by applying the appropriate kernel form.
We present the first determination of the $x$-dependent pion gluon distribution from lattice QCD using the pseudo-PDF approach, on lattice ensembles with 2+1+1 flavors of highly improved staggered quarks (HISQ), generated by MILC Collaboration. We use clover fermions for the valence action and momentum smearing to achieve pion boost momentum up to 2.29~GeV on two lattice spacings $a\approx 0.12$ and 0.15~fm and three pion masses $M_\pi\approx 220$, 310 and 690~MeV.
We compare our pion and preliminary nucleon gluon results with the determination by global fits.
We present the results that are necessary in the ongoing lattice calculations of the unpolarized and polarized gluon parton distribution functions (PDFs) within the pseudo-PDF approach. We give a classification of possible two-gluon correlator functions and identify those that contain the invariant amplitude determining the gluon PDF in the light-cone $z^2\to 0$ limit. One-loop calculations have been performed in the coordinate representation and in an explicitly gauge-invariant form. We made an effort to separate ultraviolet (UV) and infrared (IR) sources of the $\ln \left(-z^2\right) $-dependence at short distances $z^2$. The UV terms cancel in the reduced Ioffe-time distribution (ITD), and we obtain the matching relation between the reduced ITD and the light-cone ITD. Using a kernel form, we get a direct connection between lattice data for the reduced ITD and the normalized gluon PDF.
We present preliminary lattice calculations of strange and charm contributions to nucleon charges and moments. The scalar charge, axial charge, tensor charge, and unpolarized first moments are calculated on five clover-on-HISQ lattices covering three lattice spacings $a=\{0.06,0.09,0.12\}$~fm and three pion masses $M_\pi=\{310,220,130\}$~MeV. We renormalize the matrix elements with nonperturbative renormalization factors then apply chiral and continuum extrapolation to obtain results in the physical limit.
Hadronic matrix elements of the QCD energy-momentum tensor can be parametrized in terms of gravitational form factors (GFFs) which, through their dependence on momentum transfer and decomposition into quark and glue contributions, encode information about the distributions of energy, angular momentum, pressure, and shear forces within a hadron spatially and amongst its constituents. We report on the progress of an ongoing program to determine the GFFs of the physical proton with full control over uncertainties and including both quark and glue contributions, providing first-principles predictions of the physical energy, spin, pressure, and shear densities. To this end, we present preliminary results of a calculation using Wilson fermions on an ensemble with a close-to-physical pion mass of 170 MeV.
The gravitational form factors (GFFs) of hadrons are the form factors of the energy momentum tensor of QCD, which quantifies how the energy, spin and mechanical properties are distributed within hadrons and how they split between the quark and gluon degrees of freedom. We use the Belifante-Rosenfeld prescription in a Lattice QCD calculation with pion mass $m_{\pi} = 450 \; \text{MeV}$ to measure the symmetric traceless gluon GFFs for hadrons of spin 0, 1/2, 1 and 3/2 (pion, nucleon, rho meson and delta baryon) for Mandelstam $t$ in the spacelike region of $0 \leq -t < 2 \; \text{GeV}^2$. By fitting the normalized GFFs using different functional forms, we extract partial gluonic contributions to the energy, pressure and shear force densities of the hadrons in the 3D and 2D Breit frames as well as in the infinite momentum frame. We also obtain estimates for their partial gluonic mass and mechanical radii.
We present the first Lattice QCD calculation of the quark and gluon trace anomaly contributions to the hadron masses, using the overlap fermion on the 2+1 flavor dynamical Domain wall quark ensemble. The result shows that the gluon trace anomaly contributes to most of the nucleon mass, and the contribution in the pion state is smaller than that in others.
The momentum subtraction scheme (MOM) and symmetric momentum subtraction scheme (SMOM) are two of the widely used intermedium schemes for the non-perturbative renormalization of the lattice bare vertices. In principle both the schemes should provide the same MS-bar results with their respective matching, while kinds of the systematic uncertainties can create certain tensions especially at finite lattice spacing. We will show our calculation with the overlap fermion at several quark masses and lattice spacings, to compare the advantage and disadvantage of both the schemes.
It's well known that the deconfinement transition temperature for $SU(N_c)$ gauge theory is almost independent of $N_c$, and the transition is first order for $N_c \ge 3$. In the real world ($N_c=3$, light quarks) it is a crossover located far away from the pure gauge value. What happens if you keep the number of fermion flavors fixed ($N_f=2$) and vary the fermion mass and $N_c$? There are multiple plausible stories, only one of which appears to be true when the systems are simulated on the lattice. There might be consequences for other simple stories people tell about confinement, chiral symmetry breaking, and the quark model.
Instanton-dyons are topological solutions of YM equations at finite temperatures.
Their semiclassical ensembles were studied by a number of methods, including
direct Monte-Carlo simulation, for SU(2) and SU(3) theories, with and without fermions.
We present these results and compare them with those from lattice studies. We also
consider two types of QCD deformations. One is by adding operators with powers of
the Polyakov line, affecting deconfinement. Another is changing quark periodicity condition, affecting the chiral transition. Another paper is using inverse direction,
from lattice configurations (with realistic quark masses) looking at zero and near-zero
Dirac modes. It turned out that those revealing the shape of the modes,
In excellent agreement with analytic instanton-dyon theory. Summarizing both we
conclude that QCD phase transitions are well described in terms of such semiclassical objects.
The phase diagram of finite-density QCD is potentially quite complex. Like other lattice models with sign problems and generalized $\mathcal PT$ symmetry, equilibrium states of lattice QCD at finite density may be inhomogeneous, with commensurate and incommensurate patterned phases. The phase structures of such models are determined by a set of interwoven concepts: $\mathcal PT$ symmetry, Lee-Yang zeros, violation of spectral positivity, Lifshitz instabilities, NP-hard complexity, and lattice duality. $\mathcal PT$ symmetry combined with lattice duality leads to models with removable sign problems in broad universality classes with rich phase structures. These models can be simulated on the lattice by standard techniques and analytical methods may be applied as well. These ideas are illustrated using models from the $i\phi^3$, $Z(2)$, $Z(3)$ and $SU(N)$ universality classes.
We study the phase structure of effective models of finite-density QCD using analytic and lattice simulation techniques developed for the study of non-Hermitian and $\mathcal{PT}$-symmetric QFTs. Finite-density QCD is symmetric under the combined operation of the charge and complex conjugation operators $\mathcal{CK}$, which falls into the class of so-called generalized $\mathcal{PT}$ symmetries. We show that $\mathcal{PT}$-symmetric quantum field theories can support patterned ground-state field configurations in the vicinity of a critical endpoint. We apply our methods to a lattice heavy quark model at nonzero chemical potential that displays patterning behavior for a range of parameters. We derive a simple approximate criterion for the formation of these patterns, which can be used with lattice results.
We present a phase diagram study of the O(4) model as an effective
theory for 2-flavor QCD. Both theories perform spontaneous symmetry
breaking with isomorphic groups, which suggests that they
belong to the same universality class. Since we are interested
in high temperature, we further assume dimensional reduction
to the 3d O(4) model, which implies topological sectors.
As conjectured by Skyrme and others, this topological charge
represents the baryon number. Hence the baryon chemical
potential mu_B appears as an imaginary vacuum angle, which can
be included in the lattice simulation without any sign problem.
We present numerical results for the critical line in the chiral
limit, and for the cross-over in the presence of light quark masses.
The shapes of these lines are compatible with other predictions, but
up to about mu_B = 300 MeV we did not find a Critical Endpoint,
although there are indications that it could be near-by.
We investigate the distribution of energy-momentum tensor (EMT) around a static quark in the deconfined phase of SU(3) Yang-Mills theory. The EMT defined through the gradient-flow formalism is used for the numerical analysis of the EMT distribution around the Polyakov loop with the continuum extrapolation. Using EMT, one can study the mechanical distortion of the color gauge field induced by the static charge. We find substantial separation in the absolute values of the EMT eigenvalues which is not observed in Maxwell theory. The separation grows as temperature is lowered toward the critical temperature. The lattice data also indicate the thermal screening at long distance and the perturbative behavior at short distance.
We study the nature of the phase transition at high temperature and high density in lattice gauge theories by focusing on the probability distribution function, which represents the probability of appearance of particle density in a heat bath. The probability distribution function is obtained by constructing a canonical partition function by fixing the number of particles from the grand partition function. However, if the Z(3) center symmetry, which is important for understanding the finite temperature phase transition of SU(3) lattice gauge theory, is strictly maintained on a finite lattice, the probability distribution function is always zero, except when the number of particles is a multiple of 3. For U(1) gauge theory, this problem is more extreme. The center symmetry makes it impossible for a charged state to exist.
In this study, we discuss the solution to this problem, and at the same time, propose a method of avoiding the sign problem, which is an important problem in the finite density lattice gauge theory, by the center symmetry. This problem is essentially the same as the problem that the expectation value of the Polyakov loop is always zero when calculating with finite volume, as long as the center symmetry is not broken. In the U(1) lattice gauge theory, when the fermion mass is heavy, numerical simulations are actually performed, and it is demonstrated that the calculation of the probability distribution function at a finite density is possible using the method proposed in this study. Furthermore, the application of this method to QCD is discussed.
As a new algorithm towards solving the sign problem, we propose the "worldvolume tempered Lefschetz thimble method" (WV-TLTM) [1]. In this algorithm, we make hybrid Monte Carlo updates on a continuum set of integration surfaces foliated by the antiholomorphic gradient flow ("the worldvolume of the integration surface"). This algorithm is an extension of the tempered Lefschetz thimble method (TLTM) [2]. It tames the sign and multimodal problems simultaneously as the original TLTM. Furthermore, one no longer needs to prepare replicas of configuration space or compute the Jacobian of the flow except for the evaluation of its phase upon measurement, which reduces the computational cost significantly compared to the original TLTM. We apply this algorithm to the Stephanov model (a chiral random matrix model), for which the complex Langevin method is known not to work. We also discuss the effect of choosing a specific flow time region on the estimation of observables, especially by analyzing the autocorrelation times and the statistical errors [3].
[1] M. Fukuma and N. Matsumoto, "Worldvolume approach to the tempered Lefschetz thimble method," PTEP 2021, no.2, 023B08 (2021) [arXiv:2012.08468 [hep-lat]].
[2] M. Fukuma and N. Umeda, "Parallel tempering algorithm for integration over Lefschetz thimbles," PTEP 2017, no.7, 073B01 (2017) [arXiv:1703.00861 [hep-lat]].
[3] M. Fukuma, N. Matsumoto, and Y. Namekawa, in preparation.
Abstract: The SU(3) Yang-Mills matrix model coupled to fundamental
fermions is an approximation of quantum chromodynamics (QCD) on a
3-sphere of radius R. The spectrum of this matrix model Hamiltonian
estimated using standard variational methods, and is analyzed in the
strong coupling limit. By employing a renormalization prescription to
determine the dependence of the Yang-Mills coupling and the bare quark
masses on R, we relate the asymptotic values of the energy eigenvalues
in the flat space limit to the masses of light hadrons. We find that the
matrix model estimates the light hadron spectrum fairly accurately, with
most masses falling within 15% of their observed values
Lattices on Spherical Manifolds or on the cylindrical boundary of Anti-de-Sitter
space have the potential to explore non-perturbative conformal or near conformal
gauge theories for BSM studies for composite Higgs or Dark Matter. We report
on progress in the use of Quantum Finite Elements (QFE) to address renormalization on maximally symmetric spherical simplicial manifolds. The simplicial Lagrangians for scalar, Fermionic and gauge fields are found and high precision test of counter term to restore exact isometries for the 2d and 3d Ising CFT are presented. The challenges in extend QFE software to high perfomance for 4d Gauge theories on R x S3 are discussed.
We present the necessity of counter terms for Quantum Finite Element (QFE) simulations of $\phi^4$ theory on non-trivial simplicial manifolds with semi-regular lattice spacing. In particular, by computing the local cut-off dependence of UV divergent diagrams we found that the symmetries of the continuum theory are restored for $\phi^4$ theory on the manifolds $\mathbb{S}^2$ and $\mathbb{R} \times \mathbb{S}^2$. Here we consider the construction of non-perturbative local counter terms in an attempt go to larger dimensionless lattice coupling closer to the strong coupling Wilson-Fisher IR fixed point.
We explore holography with geometry fluctuation in the two-dimensional hyperbolic lattice. We present results on the behavior of the boundary-boundary correlation function of scalar fields propagating on discrete 2D random triangulations with the topology of a disk. We use a gravitational action that includes a curvature squared operator which favors a regular tessellation of hyperbolic space for large values of its coupling. An ensemble of such geometries is generated for different values of the coupling using Monte Carlo simulation. We show that the conformal behavior expected for a uniform hyperbolic space survives as this coupling is decreased implying that holographic predictions survive at least weak quantum gravity corrections. We investigated the dependency of the scaling exponent of the correlators on the mass as we vary the coupling of the curvature-squared-operator. Finally, we discuss the extension of this model to allow for the inclusion of matter field interactions and backreaction on the geometry.
We consider a massive fermion system having a curved domain-wall
embedded in a square lattice.
As already reported in condensed matter physics, the massless chiral edge modes
appearing at the domain-wall feel "gravity" through the induced spin
connections.
In this work, we embed $S^1$ and $S^2$ domain-wall into Euclidean space
and show how the gravity is detected from the spectrum of the Dirac operator.
We also discuss how we can understand gravitational anomaly inflow
and index theorem with nontrivial curvature of the domain-wall.
We analyze the chiral phase transition of the Nambu–Jona-Lasinio model in the cold and dense region on the lattice developing the Grassmann version of the anisotropic tensor renormalization group algorithm. The model is formulated with the Kogut–Susskind fermion action. We use the chiral condensate as an order parameter to investigate the restoration of the chiral symmetry. The first-order chiral phase transition is clearly observed in the dense region at vanishing temperature with μ/T〜O(10^3) on a large volume of V=1024^4. We also present the results for the equation of state.
We make an analysis of the two-dimensional U(1) lattice gauge theory with a θ term by using the tensor renormalization group.
Our numerical result for the free energy shows good consistency with the exact one at finite coupling constant. The topological charge density generates a finite gap at θ=π toward the thermodynamic limit.
In addition finite size scaling analysis of the topological susceptibility up to V=1024×1024 allows us to determine the phase transition at θ=π is the first order.
We investigate the metal-insulator transition of the (1+1)-dimensional Hubbard model in the path-integral formalism with the tensor renormalization group method. The critical chemical potential $\mu_{\rm c}$ and the critical exponent $\nu$ are determined from the $\mu$ dependence of the electron density in the thermodynamic and zero-temperature limit. Our results for $\mu_{\rm c}$ and $\nu$ show consistency with the exact solution based on the Bethe ansatz. Our encouraging results indicate the applicability of the tensor renormalization group method to the analysis of higher-dimensional Hubbard models.
Quark confinement mechanism is one of unsolved important problems in QCD. In the dual Meissner picture of color confinement, it is considered that the color flux tube between static quarks is caused by the condensation of color magnetic monopoles in the QCD vacuum. In this talk, we show new results of the dual Meissner effect due to the violation of non-Abelian Bianchi identity corresponding to Abelian Dirac-type monopoles in QCD. In particular, we discuss the vacuum type by evaluating the Ginzburg-Landau parameter through the measurements of Abelian electric field and Abelian squared monopole density in SU(3) gauge theory without gauge fixing.
The dual superconductor picture is one of the most promising scenarios for quark confinement. To investigate this picture in a gauge-invariant manner, we have proposed a new formulation of Yang-Mills theory on the lattice, named the decomposition method, so that the so-called restricted field obtained from the gauge-covariant decomposition plays the dominant role in quark confinement. It was known by preceding works that the restricted field dominance is not observed for the Wilson loop in higher representations if the restricted part of the Wilson loop is extracted by adopting the Abelian projection or the field decomposition naively in the same way as in the fundamental representation.
Recently, by the non-Abelian Stokes theorem (NAST) for the Wilson loop operator, we have proposed suitable gauge-invariant operators constructed from the restricted field to reproduce the correct behavior of the original Wilson loop averages for higher representations. We have demonstrated the numerical evidence for the restricted field dominance in the string tension, which means that the string tension extracted from the restricted part of the Wilson loop reproduces the string tension extracted from the original Wilson loop.
In this talk, we focus on the magnetic monopole. According to this picture, magnetic monopoles causing the dual superconductivity are regarded as the dominant degrees of freedom responsible for confinement. With the help of the NAST, we can define the magnetic monopole and the string tension extracted from the magnetic-monopole part of the Wilson loop in a gauge-invariant manner. We will further perform lattice simulations to measure the static potential for quarks in higher representations using the proposed operators and examine the magnetic monopole dominance in the string tension, which means that the string tension extracted from the magnetic-monopole part of the Wilson loop reproduces the true string tension from the original Wilson loop.
We review some highlights of the centre vortex research programme conducted by the CSSM in SU(3) lattice gauge theory. Starting from the original Monte Carlo gauge fields, a vortex identification procedure yields vortex-removed and vortex-only backgrounds. The original, vortex-removed, and vortex-only ensembles are compared by examining a number of different quantities. The removal of vortices consistently results in the removal of the corresponding feature associated with confinement or dynamical chiral symmetry breaking. Remarkably, we observe that after some smoothing, the vortex-only degrees of freedom are able to encapsulate the pertinent features of the original gauge fields.
This presentation examines the centre-vortex structure of Monte-Carlo generated gauge-field configurations using modern visualisation techniques. This time, the manner in which light dynamical fermion degrees of freedom impact the centre-vortex structure is explored. Focusing on the thin vortices identified by plaquettes having a non-trivial centre phase, the vortex structure is illustrated through 3D renderings of oriented spatial plaquettes. Time-oriented plaquettes are illustrated by identifying spatial links associated with these non-trivial plaquettes. The impact of light dynamical fermions is not subtle, changing both the density of vortices and the complexity of the vortex structures observed. The role of vortex branching points in full QCD is highlighted in the survey of results presented.
This presentation introduces new insights into the centre-vortex structure of lattice gauge fields, this time exploring the influence of dynamical fermions in the full-QCD vacuum. Calculations of both the Landau-gauge gluon propagator and the static quark potential reveal notable differences in the vortex phenomenology of pure-gauge and full-QCD simulations. Remarkably, configurations composed of centre-vortices alone have the ability to reproduce the static quark potential of full QCD. Moreover, the distribution of vortices in the vacuum is altered significantly with the introduction of dynamical fermions. Together, these results report the substantial influence of dynamical fermions on the centre-vortex structure of QCD-vacuum fields.
The important role of center vortices in dynamical chiral symmetry breaking and corresponding dynamical mass generation has been demonstrated in quenched studies of the Landau gauge quark propagator. We present the results of our investigation into the impact of center vortex removal on the Landau gauge quark propagator computed with overlap fermions on dynamical gauge fields. Upon removal of vortices we find that dynamical mass generation essentially vanishes, and the quark renormalization function remains flat except in the infrared where it exhibits significant suppression.
A novel method is proposed to determine the quark-diquark potential together with quark and diquark masses in the framework of Lattice Quantum Chromo Dynamics (LQCD). Treating a baryon as a quark-diquark bound state, we construct the corresponding two-body potential from the equal-time quark-diquark Nambu-Bethe-Salpeter (NBS) wave function by demanding it to satisfy the Schroedinger equation. In so doing, the quark and diquark masses in the kinetic term of the Schroedinger equation must be determined self-consistently since their direct measurement is hampered by the color confinement. We determine the mass by demanding the p-wave excitation energy obtained from the Schroedinger equation to be equal to that obtained from the two-point correlator. After examining that the formalism gives results consistent with those of the prior works in the $c\bar c$ sectors, we consider the $\Lambda_c$ baryon sector to obtain the diquark mass and the quark-diquark potential. Numerical calculations are performed on a $32^3\times64$ lattice with a cutoff of $a \simeq 0.0907$ [fm] with the pion mass of $m_{\pi}\simeq 700$[MeV] generated by PACS-CS Collaboration. The charm quark mass in this work is $m_c=1.771(48)$ [GeV] and the diquark mass is $m_D=1.220(45)$ [GeV]. The latter lies above the naive estimations such as the $\rho$ meson mass $M_\rho=$1.098(5) [GeV] and two-third of the nucleon mass $2m_N/3$=1.049(12) [GeV].
We study chirality of staggered quarks on the Dirac eigenvalue spectrum using deep learning techniques. The theory expects a characteristic pattern (we call it "leakage pattern") in the matrix elements of the chirality operator sandwiched between two eigenstates of staggered Dirac operator. Deep learning analysis gives 99.4(24)% accuracy per a single normal gauge configuration and 0.998 AUC (Area Under ROC Curve) for classifying non-zero eigenmode quartets in the Dirac eigenvalue spectrum. It confirms that the leakage pattern is universal on normal gauge configurations. We choose the multi-layer perceptron (MLP) method which is one of the deep learning models. It happens to give the best performance in our study. Numerical study is done using HYP staggered quarks on the 20^4 lattice in quenched QCD.