The analytic properties of the quark propagator from an effective infrared interaction model

TL;DR

This paper investigates the analytic structure of the quark propagator using a simplified Dyson-Schwinger equation model, employing GPU-based numerical methods to identify over 6500 poles relevant for bound state calculations.

Contribution

It introduces a novel GPU-accelerated numerical technique to analyze the complex pole structure of the quark propagator within a simplified effective interaction model.

Findings

Identified over 6500 poles in the quark propagator within the studied domain.

Grouped poles into 23 trajectories showing their movement with varying bare mass.

Provided raw data for parametrizing the quark propagator solutions across different masses.

Abstract

In this paper I investigate the analytic properties of the quark propagator Dyson-Schwinger equation (DSE) in the Landau gauge. In the quark self-energy, the combined gluon propagator and quark-gluon vertex is modeled by an effective interaction (the so-called Maris-Tandy interaction), where the ultraviolet term is neglected. This renders the loop integrand of the quark self-energy analytic on the cut-plane -Pi < arg(x) < Pi of the square of the external momentum. Exploiting the simplicity of the truncation, I study solutions of the quark propagator in the domain x in [-5.1,0] GeV^2 X i[0,10.2] GeV^2. Because of a complex conjugation symmetry, this region fully covers the parabolic integration domain for Bethe-Salpeter equations (BSEs) for bound state masses of up to 4.5 GeV. Employing a novel numerical technique that is based on highly parallel computation on graphics processing units (GPUs), I extract more than 6500 poles in this region, which arise as the bare quark mass is varied over a wide range of closely spaced values. The poles are grouped in 23 individual 'trajectories', that capture the movement of the poles in the complex region as the bare mass is varied. The raw data of the pole locations and -residues is provided as supplemental material, which can be used to parametrize solutions of the complex quark propagator for a wide range of bare mass values and for large bound state masses. This study is a first step towards an extension of previous work on the analytic continuation of perturbative one-loop integrals, with the long-term goal of establishing a framework that allows for the numerical extraction of the analytic properties of the quark propagator with a truncation that extends beyond the rainbow by making adequate adjustments in the contour of the radial integration of the quark self-energy.