Schwinger Mechanism for Gluon Pair Production in the Presence of Arbitrary Time Dependent Chromo-Electric Field in Arbitrary Gauge

TL;DR

This paper analyzes non-perturbative gluon pair production via the Schwinger mechanism in arbitrary time-dependent chromo-electric fields, demonstrating gauge invariance and independence from the gauge fixing parameter.

Contribution

It provides a gauge-invariant calculation of gluon pair production probability in arbitrary covariant gauges for time-dependent chromo-electric fields.

Findings

Gluon pair production probability is independent of gauge fixing parameter.

The result obtained in Fynman-'t Hooft gauge is gauge invariant.

The probability expression applies to arbitrary time-dependent fields.

Abstract

We study non-perturbative gluon pair production from arbitrary time dependent chromo-electric field E^a(t) with arbitrary color index a =1,2,...8 via Schwinger mechanism in arbitrary covariant background gauge \alpha. We show that the probability of non-perturbative gluon pair production per unit time per unit volume per unit transverse momentum \frac{dW}{d^4xd^2p_T} is independent of gauge fixing parameter \alpha. Hence the result obtained in the Fynman-'t Hooft gauge, \alpha=1, is the correct gauge invariant and gauge parameter \alpha independent result.