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

TL;DR

This paper critically examines a recent derivation of gluon pair production probabilities in time-dependent chromo-electric fields, questioning its validity and highlighting potential inconsistencies in the methodology used.

Contribution

The paper provides a critical analysis of an existing exact expression for gluon pair production, challenging its derivation and the applicability of the shift theorem used in the original work.

Findings

Identifies inconsistencies in the derived probability expression.

Questions the validity of the shift theorem in this context.

Highlights the need for careful methodological scrutiny in non-perturbative QCD calculations.

Abstract

Recently the paper "Schwinger Mechanism for Gluon Pair Production in the Presence of Arbitrary Time Dependent Chromo-Electric Field" by G. C. Nayak was published [Eur. Phys. J. C 59, 715 (2009); arXiv:0708.2430]. Its aim is to obtain an exact expression for the probability of non-perturbative gluon pair production per unit time per unit volume and per unit transverse momentum in an arbitrary time-dependent chromo-electric background field. We believe that the obtained expression is open to question. We demonstrate its inconsistency on some well-known examples. We think that this is a consequence of using the so-called "shift theorem" [arXiv:hep-th/0609192] in deriving the expression for the probability. We make some critical comments on the theorem and its applicability to the problem in question.