On Gribov's supercriticality picture of quark confinement

TL;DR

This paper investigates Gribov's supercriticality scenario of quark confinement by numerically analyzing the quark propagator with pion back-reaction, finding no supporting evidence for the proposed drastic analytical change.

Contribution

The study provides numerical solutions for the quark propagator in the complex plane, introduces a new method for solving the Dyson-Schwinger equation, and challenges Gribov's supercriticality hypothesis.

Findings

No evidence supporting Gribov's supercriticality scenario.

Introduces a novel numerical method for Dyson-Schwinger equations.

Discusses new features of dynamical chiral symmetry breaking.

Abstract

Some years ago Gribov developed the so-called supercritical light quark confinement scenario. Based on physical arguments he conjectured a drastic change in the analytical properties of the quark propagator when the back-reaction of Goldstone bosons (pions) is considered. We investigate this scenario and provide numerical solutions for the quark propagator in the complex plane with and without the pion back-reaction. We find no evidence for the scenario Gribov advocated. As an aside we present a novel method to solve the quark Dyson-Schwinger equation in the complex plane and discuss new characteristics of dynamical chiral symmetry breaking in our truncation scheme.