Schwinger mechanism in linear covariant gauges

TL;DR

This paper investigates the Schwinger mechanism in linear covariant gauges within pure Yang-Mills theories, deriving and analyzing a Bethe-Salpeter equation to understand gluon mass generation and its gauge dependence.

Contribution

The authors derive a generalized Bethe-Salpeter equation for gluon mass generation in linear covariant gauges and analyze the gauge dependence of solutions using lattice data and model ansätze.

Findings

Infrared finite vertex form factors are compatible with nontrivial solutions.

Solutions vary smoothly with the gauge parameter, indicating a continuous gauge dependence.

Divergent form factors require qualitative changes away from Landau gauge.

Abstract

In this work we explore the applicability of a special gluon mass generating mechanism in the context of the linear covariant gauges. In particular, the implementation of the Schwinger mechanism in pure Yang-Mills theories hinges crucially on the inclusion of massless bound-state excitations in the fundamental nonperturbative vertices of the theory. The dynamical formation of such excitations is controlled by a homogeneous linear Bethe-Salpeter equation, whose nontrivial solutions have been studied only in the Landau gauge. Here, the form of this integral equation is derived for general values of the gauge-fixing parameter, under a number of simplifying assumptions that reduce the degree of technical complexity. The kernel of this equation consists of fully-dressed gluon propagators, for which recent lattice data are used as input, and of three-gluon vertices dressed by a single form factor, which is modelled by means of certain physically motivated Ans\"atze. The gauge-dependent terms contributing to this kernel impose considerable restrictions on the infrared behavior of the vertex form factor; specifically, only infrared finite Ans\"atze are compatible with the existence of nontrivial solutions. When such Ans\"atze are employed, the numerical study of the integral equation reveals a continuity in the type of solutions as one varies the gauge-fixing parameter, indicating a smooth departure from the Landau gauge. Instead, the logarithmically divergent form factor displaying the characteristic "zero crossing", while perfectly consistent in the Landau gauge, has to undergo a dramatic qualitative transformation away from it, in order to yield acceptable solutions. The possible implications of these results are briefly discussed.