Schwinger Mechanism for Quark-Antiquark Production in the Presence of Arbitrary Time Dependent Chromo-Electric Field

TL;DR

This paper derives an exact, non-perturbative formula for quark-antiquark production in QCD under arbitrary time-dependent chromo-electric fields, showing independence from all derivatives of the field.

Contribution

It provides the first exact evaluation of quark production in arbitrary time-dependent chromo-electric backgrounds, extending the Schwinger mechanism to dynamic fields in QCD.

Findings

Exact non-perturbative quark production formula derived

Result independent of all time derivatives of the field

Functional dependence on Casimir invariants remains the same

Abstract

We study the Schwinger mechanism in QCD in the presence of an arbitrary time-dependent chromo-electric background field $E^a(t)$ with arbitrary color index $a$=1,2,...8 in SU(3). We obtain an exact result for the non-perturbative quark (antiquark) production from an arbitrary $E^a(t)$ by directly evaluating the path integral. We find that the exact result is independent of all the time derivatives $\frac{d^nE^a(t)}{dt^n}$ where $n=1,2,...\infty$. This result has the same functional dependence on two Casimir invariants $[E^a(t)E^a(t)]$ and $[d_{abc}E^a(t)E^b(t)E^c(t)]^2$ as the constant chromo-electric field $E^a$ result with the replacement: $E^a \rightarrow E^a(t)$. This result relies crucially on the validity of the shift conjecture, which has not yet been established.