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Schwinger mechanism for gluon-pair production in the presence of arbitrary time-dependent chromo-electric field

  • Gouranga C. NayakEmail author
Regular Article - Theoretical Physics

Abstract

We study the Schwinger mechanism for gluon-pair production 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) 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, \(\frac{\mathrm{d}W}{\mathrm{d}^{4}x\,\mathrm{d}^{2}p_{\mathrm{T}}}\) , 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, \(\frac{\mathrm{d}W}{\mathrm{d}^{4}x\,\mathrm{d}^{2}p_{\mathrm{T}}}\) . We find that the exact result for non-perturbative gluon-pair production is independent of all the time derivatives \(\frac{\mathrm {d}^{n}E^{a}(t)}{\mathrm{d}t^{n}}\) , where n=1,2,…,∞, and that it has the same functional dependence on the 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 E a (t). This result relies crucially on the validity of the shift conjecture, which has not yet been established. This result may be relevant to the study of the production of a non-perturbative quark–gluon plasma at RHIC and LHC.

PACS

11.15.-q 11.15.Me 12.38.Cy 11.15.Tk 

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Copyright information

© Springer-Verlag / Società Italiana di Fisica 2008

Authors and Affiliations

  1. 1.C.N. Yang Institute for Theoretical PhysicsStony Brook University, SUNYStony BrookUSA

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