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

Abstract

We study Schwinger mechanism for gluon pair production in the presence of arbitrary time-dependent chromo-electric background field $E^a(t)$ with arbitrary color index $a$=1,2,...8 in SU(3) by directly evaluating the path integral. We obtain an exact expression for the probability of non-perturbative gluon pair production per unit time per unit volume and per unit transverse momentum $\frac{dW}{d^{4}x{d}^2{p}_T}$ from arbitrary $E^a(t)$. We show that the tadpole (or single gluon) effective action does not contribute to the non-perturbative gluon pair production rate $\frac{dW}{d^{4}x{d}^2{p}_T}$. We find that the exact result for non-perturbative gluon pair production is independent of all the time derivatives $\frac{d^n{E}^a(t)}{d{t}^n}$ where $n=1,2,....\infty$ and 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: $E^a\to E^a(t)$. This result may be relevant to study the production of a non-perturbative quark-gluon plasma at RHIC and LHC.

Comments: 13 pages latex, Published in European Physical Journal C