On the quark spectral function in QCD

TL;DR

This paper computes the non-perturbative spectral function of light quarks in 2+1 flavor QCD using spectral Dyson-Schwinger equations and lattice data, revealing pole structures and continuum features relevant for QCD transport and resonance studies.

Contribution

It introduces a novel real-time spectral calculation of light quarks in QCD combining Dyson-Schwinger equations with spectral lattice data, analyzing analytic structures and unphysical poles.

Findings

Identification of pole-like peaks in the quark spectral function

Observation of a negative scattering continuum

Conditions for unphysical complex poles in the propagator

Abstract

We calculate the spectral function of light quark flavours in 2+1 flavour vacuum QCD in the isospin-symmetric approximation. We employ spectral Dyson-Schwinger equations and compute the non-perturbative quark propagator directly in real-time, using recent spectral reconstruction results from Gaussian process regression of gluon propagator data in 2+1 flavour lattice QCD. Our results feature a pole-like peak structure at time-like momenta larger than the propagator's gapping scale as well as a negative scattering continuum, which we exploit assuming an analytic pole-tail split during the iterative solution. The computation is augmented with a general discussion of the impact of the quark-gluon vertex and the gluon propagator on the analytic structure of the quark propagator. In particular, we investigate under which conditions the quark propagator shows unphysical complex poles. Our results offer a wide range of applications, encompassing the ab-initio calculation of transport as well as resonance properties in QCD.