Bayesian analysis of quark spectral properties from the Dyson-Schwinger equation

Abstract

We report results on the quark spectral function in the Landau gauge at finite temperature determined from its Dyson-Schwinger equation. Compared to earlier quenched results [1] this study encompasses unquenched N f = 2 + 1 fermion flavors in the medium. For the reconstruction of real-time spectra we deploy a recent Bayesian approach (BR method) [2] and develop a new prior in order to better assess the inherent systematic uncertainties. We identify the quark quasi-particle spectrum and analyze the (non-)appearance of zero modes at or around the pseudo-critical temperature. In both, the fully unquenched system and a simpler truncation using a model for the gluon propagator we observe a characteristic three-peak structure at zero three-momentum. The temperature dependence of these structures in case of the gluon propagator model is different than observed in previous studies. For the back-coupled and unquenched case we find interesting modifications at and around the pseudo-critical transition temperature.

QCD at finite temperature and chemical potential from Dyson–Schwinger equations

“…which is particularly well suited for spectral reconstructions using e.g. Maximum Entropy methods (MEM), see [250][251][252] for technical details. Beyond the study of positivity, spectral functions are very interesting quantities to study.…”

“…[251]. Lower left diagram: Spectral function for a range of temperatures above Tc = 142 MeV (gluon model) [252]. Lower right diagram: Strength of the zero frequency peak [252].…”

Bayesian techniques and applications to QCD

“…Contrary to the previous two proposals it actually enforces positivity, which is a genuine piece of prior information in case of hadronic spectra in QCD. It has been argued that the principle of maximum entropy which motivates S SJ leads this prior to favor smooth spectral functions, an assertion which has however been proven incorrect [19,20].…”

“…The exploration of non-local regulators (see e.g. [19,20]), which in the language of Bayesian statistics correspond to correlated distributions among the different parameters ρ l is work in progress.…”

Spectral functions and critical dynamics of the O(4) model from classical-statistical lattice simulations

“…One interesting alternative to such reconstructions of spectral functions from lattice data, as done for the present model in Ref. [11], is given by functional approaches such as n−PI [12] and Functional Renor-malization Group (FRG) methods [13][14][15][16][17][18][19] or Dyson-Schwinger equations (DSE) [20,21], which can be analytically continued or formulated directly in the real-frequency domain. However, such approaches necessarily require truncations of an infinite set of evolution equations or equations of motion for n-point correlation functions, and thus greatly benefit from additional insights into the structure and dynamics of excitations.…”