Nonperturbative QFT in the complex momentum space

14 Jun 2023, 09:00 → 16 Jun 2023, 18:00 Europe/Dublin

Physics and Chemistry Theatre (PCT) (Maynooth University)

Jon-Ivar Skullerud, Orlando Oliveira, Paul Watts, Paulo Silva, Tobias Frederico

This workshop will focus on different approaches to nonperturbative quantum field theory (including lattice QCD, Dyson-Schwinger equations and the functional renormalisation group) and on methods for analytical continuation between Euclidean and Minkowski space results, as well as prospects for direct calculations in Minkowski space.

The workshop follows on from a similar workshop in Coimbra in September 2019.  There will be no conference fee.

Confirmed speakers

Dibyendu Bala (Bielefeld)  
David Dudal (KU Leuven)  
Yui Hayashi (Kyoto)  
Markus Huber (Giessen)  
Gastão Krein (UEP São Paulo)  
Peter Lowdon (Frankfurt)  
Pepe Rodriguez-Quintero (Huelva)  
Johannes Roth (Giessen) 
Giovanni Salmè (Rome)  
Vladimir Šauli (Czech Acad Sci)
Fabio Siringo (Catania)  
Julian Urban (MIT)  
Duifje van Egmond (Ecole Polytechnique)  
Nicolas Wink (TU Darmstadt)

Wednesday 14 June

09:00 → 10:45 Wednesday Morning Session 1: Gauge Invariance

Convener: Jon-Ivar Skullerud

09:00 Opening

Speaker: Jon-Ivar Skullerud

09:15 Gauge (in)variant spectral properties of gauge-Higgs systems.

During this talk, we consider both Abelian and non-Abelian (fundamental) Higgs theories. We first focus on the elementary field two-point correlations functions and study the gauge dependence of the spectral functions. An equivalent but gauge invariant formulation of the spectrum is worked out, including renormalization and spectral properties. We end with a proposal to a priori introduce gauge invariant variables in the path integral.

Speaker: David Dudal (KU Leuven)

Maynooth2023_dd.pdf

10:00 Different approaches to gauge-invariance in Yang-Mills theories

Abstract

An essential aspect of gauge theories is that all physical observable quantities have to be gauge-invariant. In practice, however, the explicit calculations of the S-matrix elements and corresponding cross sections are done by employing the non-gauge-invariant elementary fields. This is not always problematic, as sometimes gauge independence is guaranteed by symmetry identities. In other cases, however, gauge-invariance has to be implemented. In this talk I will discuss two different ways to do so: one based on the Fröhlich-Morchio-Strocchi conjecture for the electroweak theory, another based on recent work on the centersymmetric Landau gauge, which leaves essential physical symmetries intact after gauge-fixing.

Speaker: Dr Duifje van Egmond (Ecole Polytechnique, Palaiseau)

Maynooth_duifje.pdf

10:45 → 11:15 Coffee Break

11:15 → 12:45 Wednesday Morning Session 2: Complex Singularities I

11:15 Reconstruction and interpretation of propagators with complex singularities

Several theoretical models and recent numerical studies propose the existence of complex singularities in propagators of confined particles, specifically the Landau-gauge gluon propagator. Such singularities are beyond the conventional framework of quantum field theory, necessitating a detailed analysis of the reconstruction from Euclidean to Minkowski propagators. This talk will present our rigorous studies on this reconstruction when complex singularities exist. We show that the analytically continued Wightman function is holomorphic in the standard tube, and the Lorentz symmetry and locality are maintained. On the other hand, the reconstructed Wightman function violates the temperedness and positivity condition. Lastly, we discuss possible quantum mechanical interpretations and their implications on confinement mechanism.

Speaker: Yui Hayashi (YITP, Kyoto University)

hayashi.pdf

12:00 On the analytic structure of three-point functions from contour deformations

Contour deformations are a useful tool to perform calculations for complex momenta in Euclidean metric. An application is the calculation of elementary correlations of quarks and gluons. In the case of propagators, it is already used and applied to different cases. However, due to the more complicated kinematics, the situation is different for vertices for which this technique is hardly explored. In this talks, the generalizations necessary for three-point functions are discussed. Contact to the Landau conditions is made which give the positions of branch cuts of integrals. As an example, the emergence of branch cuts in nonperturbative calculations of $\phi^3$ theory is discussed.

Speaker: Markus Huber

Maynooth2023.pdf

12:45 → 14:00 Lunch

14:00 → 15:30 Wednesday Afternoon Session: Complex Singularities II

14:00 Are the Gluon Complex Poles Real?

The existence of genuine complex conjugated poles in the gluon propagator is discussed together with the problems that the complex poles would raise.

In the first part, some arguments in favour of their existence are presented. Their appearance in different approaches is reviewed and some features of the complex poles are related to confinement, string tension and condensates.

In the second part, some of the problems raised by the complex-conjugated poles are examined. Notably, the standard Wick rotation and the Kallén-Lehmann representation would be invalidated, thus questioning the physical meaning of the theory and even casting doubts on the existence of a meaningful theory in Minkowski space. A speculative way to solve the main problems is proposed, yielding a modified spectral representation and a relation between the complex poles and the physical spectrum.

Speaker: Fabio Siringo

ComplexPoles2023.pdf

14:45 Non-perturbative characteristics of spectral functions at finite temperature

For QFTs at finite temperature spectral functions describe how particle systems behave in the presence of a thermal medium. Here we report on recent progress regarding the non-perturbative constraints imposed by causality on these objects, and discuss how this information can be used to extract spectral properties from Euclidean data.

Speaker: Peter Lowdon

Maynooth_Lowdon.pdf

15:30 → 16:00 Coffee Break

16:00 → 17:00 Wednesday Discussion

Convener: David Dudal (KU Leuven)

Thursday 15 June

09:15 → 10:45 Thursday Morning Session 1: Hadron Properties I

09:15 Spectral reconstruction with Gaussian processes

By extending standard Gaussian process regression to inference from indirect observations, one obtains a powerful non-parametric algorithm for the probabilistic treatment of ill-conditioned linear inverse problems. This makes it a promising ansatz for Fredholm integral inversion, of which the spectral reconstruction of correlation functions in quantum field theory is a particular instance. The approach allows to directly incorporate arbitrary linear operator constraints such as sum rules; furthermore, analytically known asymptotics of the spectral function can be included by applying Mercer's theorem for positive semi-definite kernels. In this talk, I will introduce the algorithm, discuss its relation to the Backus-Gilbert method, and present two applications: 1. The reconstruction of 2+1 flavor lattice QCD data for ghost and gluon propagators as well as the strong coupling constant. 2. The extraction of glueball masses from timelike interaction channels of the four-gluon vertex in Yang-Mills theory, computed with the functional renormalization group.

Speaker: Julian Urban

Maynooth-2023-Urban.pdf

10:00 Spectral reconstruction from lattice correlator

In this talk, I will discuss spectral reconstruction from various lattice correlators, with a primary focus on spectral reconstruction related to photon production rates.

Thermal photons are a vital tool for studying the Quark-Gluon Plasma (QGP). The photon production rate from the plasma at temperature is proportional to the transverse spectral function $\rho_T(\omega,\vec k)$. The photon production rate can be calculated from the difference between the transverse $\rho_T(\omega,\vec k)$ and longitudinal $\rho_L(\omega,\vec k)$ correlators, as $\rho_L$ vanishes at the light cone. The UV part of $\rho_T(\omega,\vec k)-\rho_L(\omega,\vec k)$ is suppressed, resulting in the Euclidean correlator primarily capturing contributions from the IR part of $\rho_T(\omega,\vec k)-\rho_L(\omega,\vec k)$. To explore these concepts, we calculate the T-L correlator on $N_f=2+1$ flavor Highly Improved Staggered Quark (HISQ) configurations, as well as on quenched QCD. We showcase various methods of spectral reconstruction from these correlators and compare the estimated photon production rates obtained.

Additionally, I will discuss other ongoing research that requires spectral reconstruction. I will touch upon topics such as the thermal static quark-antiquark potential, pseudo scalar spectral function for quarkonium, and heavy quark diffusion coefficients.

Speaker: Dibyendu Bala (Bielefeld University)

Dibyendu_.pdf

10:45 → 11:15 Coffee Break

11:15 → 12:45 Thursday Morning Session 2: Hadron Properties II

11:15 Pion GPDs and GFFs from data and DSE

Speaker: José Rodríguez-Quintero

CQFT-PpRQ.pdf

12:00 Light cone parton distributions from lattice quantum chromodynamics

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 and the pion addressing among others 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.
Finally, we will present the latest results of the HadStruc collaboration on the gluon, helicity and transversity PDF of the nucleon.

Speaker: Savvas Zafeiropoulos

Zafeiropoulos_Maynooth23.pdf

12:45 → 14:00 Lunch

14:00 → 15:30 Thursday Afternoon Session: Hadron Properties III

14:00 Matter distribution in the proton -- the gluon scalar form factor

I will discuss the gluon scalar form factor of the proton and its relation to the QCD trace anomaly and the origin of the proton mass. After reviewing calculations of this form factor using different models, I will discuss the prospects of its experimental extraction using femtoscopic measurements of the Jpsi-proton interaction. I will finish with a brief discussion about the corresponding gluonic form factor of the pion.

Speaker: Prof. Gastao Krein

gkrein_Maynooth.pdf

14:45 Pion momentum distributions in Minkowski space

We present a dynamical model for the pion based on the solution of the Bethe-Salpeter equation in Minkowski space. The masses of quark and gluon as well as the interaction-vertex scale have been chosen in a range suggested by lattice-QCD calculations, and calibrated to reproduce both pion mass and decay constant. Within this model, we obtain the valence probability, the LF-momentum distributions, the distribution amplitudes, the probability densities both in the LF-momentum space and the 3D space given by the Cartesian product of the covariant Ioffe-time and transverse coordinates [1] and the pion electromagnetic form factor, with a good agreement with available experimental data [2]. In addition, we obtain the parton distribution function [3] and show that, after performing an evolution with an effective charge and a LO splitting function, our outcomes agree with the extracted experimental data (with resummation effects). Finally, the unpolarized twist-2 (leading) and twist-3 (subleading), T-even, transverse-momentum dependent quark distributions in the pion are evaluated [4].

References:
1.W. de Paula, E. Ydrefors, J. H. Alvarenga Nogueira, T. Frederico and G. Salme, Phys. Rev. D 103 (2021) no.1, 0140022. E. Ydrefors, W. de Paula, J. H. A. Nogueira, T. Frederico and G. Salme, Phys. Lett. B 820 (2021), 136494
3. W. de Paula, E. Ydrefors, J. H. Alvarenga Nogueira, T. Frederico and G. Salme, Phys. Rev. D 105 (2022) L071505
4. E. Ydrefors, W. de Paula, T. Frederico and G. Salme, arXiv:2301.11599

Speaker: Prof. wayne de paula (Instituto Tecnologico de Aeronautica)

NpQFTdePaula.pdf

15:30 → 16:00 Coffee Break

16:00 → 17:00 Thursday Discussion

Convener: Gastao Krein

Friday 16 June

09:15 → 10:45 Friday Morning Session 1: Calculations in Minkowski Space I

09:15 Real-time functional renormalization group and critical dynamics

The functional renormalization group (FRG) formulated in real time on the Schwinger-Keldysh closed-time path provides an excellent calculational tool for real-time quantities such as spectral functions and transport coefficients, and in particular for their universal static and dynamic scaling behavior near a critical point. In this talk I will present the novel formulation of FRG flows in Minkowski spacetime, which consists of interpreting the corresponding causal regulator as a coupling to a fictitious external heat bath with FRG scale dependent spectral distribution. As particular applications, I will give a brief overview on some of the dynamic universality classes relevant for QCD, and outline how they can be implemented within the real-time FRG. With this setup, I will present results demonstrating the generation of dynamic scaling behavior in spectral functions obtained from one and two-loop self-consistent truncation schemes.

Speaker: Johannes Roth

Roth.pdf

10:00 Spectral functions from the functional formalism of spectral gap equations

I will talk about the reflections of confinement phenomena as seen in the solution for the gluon and the quark propagators in the Minkowski space formalism of QCD gap equations. Further, the solution and its gauge dependence will be shown in the case of walking gauge theory.

Speaker: Mr Vladimir Sauli

Sauli.pdf

10:45 → 11:15 Coffee Break

11:15 → 12:00 Friday Morning Session 2: Calculations in Minkowski Space II

11:15 Accessing Yang-Mills in the complex momentum plane with the spectral DSE

In this talk, I'll discuss how Dyson-Schwinger equations can be analytically continued, using the spectral DSE.
Hereby, spectral representations are inserted into the equations, making the use of dimensional regularization, and hence, analytic continuation at the level of the equations feasible.
Applications to the ghost and gluon in Yang-Mills are presented.

Speaker: Nicolas Wink (TU Darmstadt)

Wink.pdf

12:00 → 13:00 Friday Discussion

Convener: Markus Huber