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

• Published in: The European physical journal. C, Particles and fields Particles and fields, 2009-02, Vol.59 (3), p.715-722, Article 715
• Main Author: Nayak, Gouranga C.
• Format: Article
• Language: English
• Subjects: Astronomy; Astrophysics and Cosmology; Electric fields; Elementary Particles; Exact sciences and technology; Gluons; Hadrons; Heavy Ions; Large Hadron Collider; Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Pair production; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quark-gluon plasma; Regular Article - Theoretical Physics; String Theory; The physics of elementary particles and fields; Time dependence; Transverse momentum
• ISSN: 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-008-0819-8

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, , 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, . We find that the exact result for non-perturbative gluon-pair production is independent of all the time derivatives , 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.