A machine learning pipeline for autonomous numerical analytic continuation of Dyson-Schwinger equations

Dyson-Schwinger equations (DSEs) are a non-perturbative way to express n-point functions in quantum field theory. Working in Euclidean space and in Landau gauge, for example, one can study the quark propagator Dyson-Schwinger equation in the real and complex domain, given that a suitable and tractable truncation has been found. When aiming for solving these equations in the complex domain, that is, for complex external momenta, one has to deform the integration contour of the radial component in the complex plane of the loop momentum expressed in hyper-spherical coordinates. This has to be done in order to avoid poles and branch cuts in the integrand of the self-energy loop. Since the nature of Dyson-Schwinger equations is such, that they have to be solved in a self-consistent way, one cannot analyze the analytic properties of the integrand after every iteration step, as this would not be feasible. In these proceedings, we suggest a machine learning pipeline based on deep learning (DL) approaches to computer vision (CV), as well as deep reinforcement learning (DRL), that could solve this problem autonomously by detecting poles and branch cuts in the numerical integrand after every iteration step and by suggesting suitable integration contour deformations that avoid these obstructions. We sketch out a proof of principle for both of these tasks, that is, the pole and branch cut detection, as well as the contour deformation.

Correlations and Critical Behavior in Lattice Gluodynamics

In the Landau-gauge lattice gluodynamics we find that, both in the SU(2) and SU(3) theory, a correlation of the Polyakov loop with the asymmetry of the A2 gluon condensate as well as with the longitudinal propagator makes it possible to determine the critical behavior of these quantities. We discuss finitevolume corrections and reveal that they can be reduced by the use of regression analysis. We also analyze the temperature dependence of low-momenta propagators in different Polyakov-loop sectors.

Gauge-fixed Lattice QCD and the dispersion relation of Wilson fermions

We show that, when investigating Wilson-fermions correlation functions on the lattice, one is bound to encounter major difficulties in defining their dispersion relation, even at tree level. The problem is indeed quite general and, although we stumbled upon it while studying Coulomb-gauge applications, it also affects gauge fixed studies in covariant gauges, including their most popular version, Landau gauge. In this paper we will discuss a solution to this problems based on a redefinition of the kinematic momentum of the fermion.

Another look at the Landau gauge three-gluon vertex

We revisit the computation of the three-gluon vertex in the Landau gauge using lattice QCD simulations with large physical volumes of ~ (6.5 fm)4 and ~ (8 fm) 4 and large statistical ensembles. For the kinematical configuration analysed, that is described by a unique form factor, an evaluation of the lattice artefacts is also performed. Particular attention is given to the low energy behavior of vertex and its connection with evidence (or lack of it) of infrared ghost dominance.

Discriminating Chiral Insertions from BSM for the Muon (g-2) by non-Abelian Zero Modes

A sorting out method, between the New Physics and as vs. the Lepton Flavor Violated Chiral insertion is exposed, interpreting so the Light-by-Light scattered amplitude deviation in the muon magnetic moment, with a novel 2-color instead of 3-color in diagrams projective polarizations. The calculation is done using an extension-detention of the muon resonance interaction internal lines (which may be generically of a non-QCD nature)such its modes’ phonons decompose into instantons while the helicities are to meet the imposed polarizations. A confirmation comes out from a non-applicability of the Landau Gauge, to the one of the cases, the tri-vector-mode, giving it a double pole in its Goldstone propagator, vs. its truth in the Sudakov type with a single pole mode Goldstone propagator.The fits between expansions of the phonon derived from slicing’s, and the instanton derived from inverse arguments of differently coupled cosine’s, are surprisingly proportional to their projected (2 to 3 in their extended diagrams) normalization factors paving ways into a BSM popped up selectivity method.

A window on infrared QCD with small expansion parameters

Lattice simulations of the QCD correlation functions in the Landau gauge have established two remarkable facts. First, the coupling constant in the gauge sector — defined, e.g., in the Taylor scheme— remains finite and moderate at all scales, suggesting that some kind of perturbative description should be valid down to infrared momenta. Second, the gluon propagator reaches a finite nonzero value at vanishing momentum, corresponding to a gluon screening mass. We review recent studies which aim at describing the long-distance properties of Landau gauge QCD by means of the perturbative Curci-Ferrari model. The latter is the simplest deformation of the Faddeev-Popov Lagrangian in the Landau gauge that includes a gluon screening mass at tree-level. There are, by now, strong evidences that this approach successfully describes many aspects of the infrared QCD dynamics. In particular, several correlation functions were computed at one- and two-loop orders and compared with ab-initio lattice simulations. The typical error is of the order of ten percent for a one-loop calculation and drops to few percents at two loops. We review such calculations in the quenched approximation as well as in the presence of dynamical quarks. In the latter case, the spontaneous breaking of the chiral symmetry requires to go beyond a coupling expansion but can still be described in a controlled approximation scheme in terms of small parameters. We also review applications of the approach to nonzero temperature and chemical potential.

Gluon propagators in $$2+1$$ lattice QCD with nonzero isospin chemical potential

The static longitudinal and transverse gluon propagators in the Landau gauge are studied in $$2+1$$ 2 + 1 lattice QCD with nonzero isospin chemical potential $$\mu _I$$ μ I . Parameterization of the momentum dependence of the propagators is provided for all values of the chemical potential under study. We find that the longitudinal propagator is infrared suppressed at nonzero $$\mu _I$$ μ I with suppression increasing with increasing $$\mu _I$$ μ I . It is found, respectively, that the electric screening mass is increasing with increasing $$\mu _I$$ μ I . Additionally, we analyze the difference between two propagators as a function of the momentum and thus compare interactions in chromoelectric and chromomagnetic sectors.