### Conveners

#### QCD at nonzero Temperature and Density

- Biagio Lucini (Swansea University)

#### QCD at nonzero Temperature and Density

- Alexei Bazavov (Michigan State University)

#### QCD at nonzero Temperature and Density

- Jana N. Guenther (Aix Marseille University)
- Claudia Ratti (University of Houston)

#### QCD at nonzero Temperature and Density

- Victor Braguta (ITEP)

#### QCD at nonzero Temperature and Density

- Kazuyuki Kanaya (University of Tsukuba)

#### QCD at nonzero Temperature and Density

- Sayantan Sharma
- Claudio Bonati (University of Pisa and INFN)

#### QCD at nonzero Temperature and Density

- Gergely Endrodi (University of Bielefeld)

#### QCD at nonzero Temperature and Density

- Akio TOMIYA (Osaka university)

#### QCD at nonzero Temperature and Density

- Heng-Tong Ding (Central China Normal University)
- Hiroshi Ohno (Center for Computational Sciences, University of Tsukuba)

#### QCD at nonzero Temperature and Density

- Alexander Rothkopf (University of Stavanger)
- Maria Paola Lombardo (INFN)

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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,...

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...

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...

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...

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...

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...

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...

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...

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 $\mu_B$....

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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,...

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 $\mathcal{PT}$...

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...

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...

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...

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...

I outline the simulation of lattice QCD with $N_f=2+1+1$ optimal domain-wall quarks at the physical point, on the $64^3 \times (6,8,10,12,16,20) $ lattices, for three lattice spacings $a \sim 0.064-0.075$ fm. The quark masses and lattice spacings are determined at the zero temperature on the $64^4$ lattice. The topological susceptibility of each gauge ensemble is measured by the Wilson flow....

Simulations for the thermodynamics of the 2+1 flavor QCD are performed employing chiral fermions. The use of Möbius domain wall fermions with stout-link smearing is most effective in the finer lattices where the relevant SU(2) and U(1) chiral symmetries in the chiral limit is approximated to higher degree in the simulation. We report on an initial attempt to locate the (pseudo) critical point...

The axial U(1) anomaly in high-temperature QCD plays an important role to understand the phase diagram of QCD. The previous works by JLQCD Collaboration studied high-temperature QCD using 2-flavor dynamical chiral fermions, such as the domain-wall fermion and reweighted overlap fermion. We extend our simulations to QCD with 2+1 flavor dynamical quarks, where the masses of the up, down, and...

In this talk we present the novel relations between the quark mass derivatives [$\partial^{n}\rho(\lambda,m_l)/\partial m_{l}^{n}$] of the Dirac eigenvalue spectrum and the $(n+1)$-point correlations among the eigenvalues. Using these relations we present lattice QCD results for $\partial^{n}\rho(\lambda,m_l)/\partial m_{l}^{n}$ ($n=1, 2, 3$) for $m_l$ corresponding to pion masses...

Dirac Eigenvalue spectrum $\rho$ and its derivatives with respect to quark mass are useful quantities to study the microscopic origin of the chiral symmetry breaking in QCD. It has been proposed in Ref.[1] that the n-th order derivative of Dirac eigenvalue spectrum with respect to quark mass $\partial^n\rho/\partial m^n$ is connected to the (n+1)-point correlation function among Dirac...

We present preliminary lattice results for the topological susceptibility in high-temperature $N_f=2+1$ QCD obtained discretizing this observable via spectral projectors on eigenmodes of the staggered operator, and we compare them with those obtained with the standard gluonic definition.

The adoption of the spectral discretization is motivated by the large lattice artifacts affecting the...

I show that a finite density of near-zero localised Dirac modes can lead to the disappearance of the massless excitations predicted by the finite-temperature version of Goldstone's theorem in the chirally-broken phase of a gauge theory.

It is known that the deconfining transition of QCD is accompanied by the

appearance of localized eigenmodes at the low end of the Dirac spectrum. In

the quenched case localization appears exactly at the critical temperatura of

deconfinement. In the present work, using quenched simulations exactly at the

critical temperature we show that the localization properties of low Dirac

modes...

One consequence of the recently developed effective number theory, designed to count objects with probabilities, is that it leads to a well-defined concept of *effective dimension*. Due to the additivity of effective numbers, the latter is a measure-based construct extending the Hausdorff/Minkowski-like notion of dimension for fixed sets (with metric) to the stochastic domain. Both IR...

We will show mesonic ground masses at increasing temperatures for different flavour structures and operators. The mass extraction is carried out using a fitting procedure on anisotropic thermal correlation functions. We use FASTSUM collaboration thermal ensembles corresponding to an anisotropy of $\xi = 3.5 = a_\tau / a_s$.

Using the meson masses as a function of the temperature, we aim to...

We compute flavor non-singlet meson screening masses in the chiral limit of QCD with $N_f=3$ quarks. The calculation is

carried out at 11 temperatures covering from $T\approx 1$ GeV up to the electroweak scale. For each temperature we simulated

4 different lattice spacings, so as to be able to perform the continuum limit extrapolation with confidence at a few permille-accuracy. The...

This report is devoted to the study of the influence of relativistic rotation on the confinement/deconfinement transition in gluodynamics within lattice simulation. We perform the simulation in the reference frame which rotates with the system under investigation, where rotation is reduced to external gravitational field. To investigate the confinement/deconfinement transition the Polyakov...

In this report, we present our results on the lattice study of the EoS of dense

QCD in an external magnetic field. The simulations are performed with

$N_f = 2+1$ rooted dynamical staggered quarks at the physical point.

Finite density is introduced through the imaginary chemical potentials

$\mu_u=\mu_d=\mu_I$, $\mu_s=0$. The EoS is obtained as series with respect

to $\mu$ up to $\mu^6$...

In this work we study the properties of $N_f=2+1$ QCD in the presence of a constant background magnetic field, up to unexplored large values of $eB$, by means of lattice Monte Carlo simulations. We investigate the string tension and its asymmetry via the study of the static quark-antiquark potential and of the color flux tube. Moreover, we present preliminary results regarding the QCD phase...

In non-central heavy-ion collisions, the magnetic fields generated are stronger than any ground-based experiments, reaching magnitudes comparable to the strong scale and being highly non-uniform. To study such extreme conditions, we simulate the theory of strong interactions at finite temperature on the lattice, with staggered fermions and an inhomogeneous magnetic background. Just as in the...

Applications of machine learning techniques to numerical studies of quantum field theories have been explored intensely in recent years. One such application is the use of a neural network for finding a map between the Boltzmann distribution of a lattice field theory and a simpler distribution function (a 'trivializing map' or 'normalizing flow'). Once such a map is found, one expects to...

We discuss the flavor number dependence of QCD at finite density by using the complex Langevin method. In our previous works, the complex Langevin method is confirmed to satisfy the criterion for correct convergence in some regions, such as $\mu / T = 5.2-7.2$ on $8^3 \times 16$ and $\mu / T = 1.6-9.6$ on $16^3 \times 32$ using $N_f = 4$ staggered quarks at $\beta = 5.7$. We extend this study...

Recent developments in methods to overcome the sign problem in finite density QCD such as the complex Langevin method give us hope to investigate color superconductivity (CSC) in cold dense QCD matter from first principles. In view of this situation, we obtain quantitative predictions for the parameter region for CSC from lattice perturbation theory, which is valid for QCD in a small box. In...

At low temperature and high density, quark matter is expected to be a color superconductor(CSC). In a recent study based on lattice perturbation theory, we have found that the CSC occurs even on a lattice with a small spatial length. According to our previous study (JHEP10(2020)144), the complex Langevin method is expected to work on such a lattice without suffering from the excursion and...

We show our lattice QCD results for masses and magnetic polarizabilities of light and strange pseudo-scalar mesons, chiral condensates, decay constants of neutral pion and neutral kaon in the presence of background magnetic fields with $eB$ ranging up to around 3.35 GeV$^2$ ($\sim70~M_\pi^2$) in the vacuum. We performed (2+1)-flavor QCD lattice simulations using the Highly Improved Staggered...

We study the second-order fluctuations of and correlations among net baryon number, electric

charge and strangeness in (2+1)-flavor QCD at non-zero magnetic field. We perform the lattice simulations using the tree-level improved gauge action and the highly improved staggered quark (HISQ) action with a fixed scale approach ($a\simeq$ 0.117 fm). The strange quark mass is fixed to its physical...

We apply the persistent homology analysis to effective models of quantum chromodynamics (QCD) with heavy quarks on a rectangular lattice to investigate the confinement-deconfinement transition. In this talk, I will concentrate on the effective Polyakov-line model and the Potts model with external field as the QCD effective model. The configurations are mapped onto the complex Polyakov-line...

Abstract: we study the confinement-deconfinement transition and $Z_2$ symmetry in lattice $Z_2+$Higgs theory in $3+1$ dimensional Euclidean space using lattice Monte Carlo simulation methods. In pure $Z_2$ gauge theory the CD transition is first order. Polyakov loop acquires non-zero thermal average value in the deconfined phase and the $Z_2$ symmetry is spontaneously broken. The $Z_2$...

Motivated by the early-time dynamics of the quark-gluon plasma in high-energy heavy-ion collisions, we extract gluonic spectral functions of overoccupied gauge theories far from equilibrium using classical-statistical lattice simulations. In 3+1 dimensions we find that the spectral function exhibits quasiparticle excitations at all momenta that are mostly consistent with perturbative...

The study of jets in heavy ion collisions provides important information about the interaction of partons with the medium that they traverse. The seeds of jets are highly energetic partons, which are produced from hard scatterings during the collision event. As such, they are affected by all different stages of the medium's time evolution, including the glasma, which is the pre-equilibrium...

We discuss the behaviour of a universal combination of susceptibility and correlation length in the Ising model in two and three dimensions, in presence of both magnetic and thermal perturbations, in the neighbourhood of the critical point. In three dimensions we address the problem using a parametric representation of the equation of state. In two dimensions we make use of the exact...

The Polyakov loop expectation value $\langle P\rangle$ is an order parameter of the deconfinement transition in the heavy quark mass regime, whereas its sensitivity to the deconfinement of light, dynamical quarks is not apparent. From the perspective of an effective Lagrangian in the vicinity of the chiral transition, the Polyakov loop, $P$, is an energy-like observable, and $\langle P\rangle$...

We study the scaling behavior of the (2+1)-QCD crossover region towards the chiral limit with smaller-than-physical light quark mass gauge ensembles, generated using the HISQ fermion discretisation. We calculate the leading curvature coefficient of the QCD crossover line at smaller light quark masses and compare it with the curvature in the chiral limit obtained using scaling arguments. At...

At finite imaginary values of the chemical potential, QCD is free of the sign

problem. Moreover, at high temperatures the partition function exhibits

a new symmetry (the Roberge-Weiss symmetry) connecting phases

with different orientations of the Polyakov loop, and the corresponding

phase transitions between these.

In this contribution we investigate the perturbative one-loop

effective...

QCD with heavy dynamical quarks exhibits a first order thermal transition which is driven by the spontaneous breaking of the global $Z_3$ center symmetry. Decreasing the quark masses weakens the transition until the corresponding latent heat vanishes at the critical mass.

We explore the heavy mass region with three flavors of staggered quarks. We analyze the Polyakov loop and its moments in a...

Effective 3d Polyakov loop theories derived from QCD by strong coupling and hopping expansions are valid for heavy quarks and can also be applied to finite chemical potential, due to their considerably milder sign problem. We apply the Monte-Carlo method to the $N_f=1,2$ effective theories up to $\mathcal{O}(\kappa^4)$ in the hopping parameter at zero $\mu$ to determine the critical quark...

Establishing whether or not the famous first order corner at small quark masses exists in the Columbia plot is one of the major open issues in studies of the phase diagram of QCD. We delve into this problem and present results from our ongoing study of the chiral limit in three-flavor QCD using the Highly Improved Staggered Quark (HISQ/tree) action.

We investigate four quark masses, which...

The Columbia plot specifies the order of the $N_f=2+1$ QCD thermal transition as a function of the quark masses. Since massless quarks cannot be simulated directly, the nature of the phase transition in the limit of vanishing $u,d$-quark masses has remained elusive, with different discretisations showing different orders of the transition in the small mass regime. We propose a modified...

Four-fermion theories are widely appreciated as toy models for QCD and are also used in numerous condensed-matter applications. We investigate such theories, namely the 1+1 dimensional (chiral) Gross-Neveu models, at finite temperature and density, where mean field studies predict the existence of inhomogeneous phases, i.e., phases where the chiral condensate has a non-trivial spatial...

In a previous work the regulator dependence of inhomogeneous phases in the $2+1$-dimensional Gross-Neveu model has been studied within the mean-field approximation. These are phases, where in addition to chiral symmetry also translational symmetry is broken. Inhomogeneous condensates are a feature shared among various strong-interaction models and not unique to the $2+1$-dimensional...

We present results for the photon emission rate determined from the transverse channel vector correlator at fixed spatial momentum using two-flavor dynamical Wilson fermions at T ~ 250 MeV. We estimate the transverse channel spectral function using the continuum extrapolated correlator by applying various fit ansätze with a smooth matching to the NLO perturbative result. We confront our...

The photon emissivity of quark-gluon plasma probes the interactions in

the medium and differs qualitatively between a weakly coupled and a

strongly coupled plasma in the soft-photon regime. The photon

emissivity is given by the product of kinematic factors and a spectral

function associated with the two-point correlator of the

electromagnetic current at lightlike kinematics. A certain...

We present our results on the study of the electromagnetic conductivity in

dense quark-gluon plasma obtained within lattice simulations with $N_f = 2 + 1$

dynamical quarks. We employ stout improved rooted staggered quarks at

the physical point and the tree-level Symanzik improved gauge action.

The simulations are performed at imaginary chemical potential and the

Backus-Gilbert method is...

In this talk we show our lattice QCD calculations for the sphaleron rate (the Minkowski rate for topological charge diffusion). It is determined by modeling the spectral function encoded in the Euclidean topological-charge-density two-point function. The Euclidean correlation functions are measured under gradient flow to reduce noise with improved operators which can more accurately measure...

We extract the heavy quark diffusion coefficient $\kappa$ and the resulting momentum broadening $\langle p^2 \rangle$ of a heavy quark embedded in a far-from-equilibrium gluon plasma using classical-statistical lattice simulations. We find several features in the time dependence of the momentum broadening: a short initial rapid growth of $\langle p^2 \rangle$, followed by linear growth with...

The heavy quark diffusion coefficient is encoded in the spectral

functions of the chromo-electric and the chromo-magnetic correlators that are

calculable on the lattice. We study the chromo-electric and the chromo-magnetic correlator in the deconfined phase of SU(3) gauge theory using Symanzik flow at

two temperatures 1.5Tc and 10000Tc, with Tc being the phase transition

temperature. To...

Heavy quark transport coefficients calculated from first-principles QCD are a crucial input for transport models. Utilizing the heavy quark limit, we will discuss the results of a novel approach to nonperturbatively estimate the heavy quark diffusion coefficient in a hot gluonic medium from gradient-flowed color-electric correlators on the lattice. Unlike others, this approach can be extended...

We study the static energy between a quark anti-quark pair in a thermal medium based on ensembles with $N_f=2+1$ dynamical HISQ flavors. Our dataset spans the phenomenologically relevant temperature range between T=140MeV-2GeV based on lattice sizes $48^3$x10,12 and 16. The real- and imaginary part of the potential is determined from the spectral function of Wilson-line correlators in Coulomb...

We have studied finite temperature complex static quark-antiquark potential for 2+1 flavor QCD using highly improved staggered action with pion mass 161 MeV. We extracted the potential using the Wilson line correlator fixed in Coulomb gauge. For the extraction, we have used a newly developed method [1] of splitting the correlator into symmetric and anti-symmetric parts. Using this method we...

We report our calculation of the inter-quark potential of bottomonium at non-zero temperature using the HAL QCD method. This is applied to NRQCD non-local correlation functions generated from anisotropic FASTSUM ensembles. The correlation functions are initially calculated in momentum space for greater efficiency. Results will be presented for the interquark potential of various states as a...

We present the Backus-Gilbert method as a means of reconstructing spectral functions from NRQCD meson correlator data at non-zero temperature. We focus in particular on the resolving power of the method, providing a demonstration of how the underlying resolution functions can be probed by exploiting the Laplacian nature of the NRQCD kernel. We conclude with estimates of the bottomonium ground...

We discuss results for bottomonium at nonzero temperature obtained using NRQCD on FASTSUM Generation 2L ensembles. We give an update on results for spectral functions obtained using Kernel Ridge Regression, paying in particular attention to the generation of training data. We compare our findings to estimates of masses of both ground- and the first excited states obtained using multi-exponential fits.