Casimir dependence of transverse distribution of pairs produced from a strong constant chromo-electric background field

TL;DR

This paper investigates how the transverse distribution of pairs produced in a strong chromo-electric field depends on gauge-invariant quantities, specifically quantifying the effect of the second Casimir invariant, C_2, which is found to be at most 15%.

Contribution

It explicitly analyzes the dependence of pair distribution on the second Casimir invariant, C_2, revealing a limited impact of at most 15%, extending previous work on gauge invariants.

Findings

Dependence on C_2 is at most 15%.

Transverse distribution primarily depends on C_1.

Quantitative analysis of gauge invariant effects.

Abstract

The transverse distribution of gluon and quark-antiquark pairs produced from a strong constant chromo-electric field depends on two gauge invariant quantities, $C_1=E^aE^a$ and $C_2=[d_{abc}E^aE^bE^c]^2$, as shown earlier in [G.C. Nayak and P. van Nieuwenhuizen, Phys. Rev. D 71, 125001 (2005)] for gluons and in [G.C. Nayak, Phys. Rev. D 72, 125010 (2005)] for quarks. Here, we discuss the explicit dependence of the distribution on the second Casimir invariant, C_2, and show the dependence is at most a 15% effect.