Soft-gluon production due to a gluon loop in a constant chromoelectric background field

Abstract

We obtain an exact result for the soft gluon production and its p T distribution due to a gluon loop in a constant chromo-electric background field E a with arbitrary color. Unlike Schwinger's result for e + e − pair production in QED which depends only on one gauge invariant quantity, the electric field E, we find that the p T distribution of the gluons depend on two gauge invariant quantities, E a E a and [d abc E a E b E c ] 2 .

Density matrix of a quantum field in a particle-creating background

“…In some articles devoted to the chromoelectric flux tube model (see, e.g., [12,14,35]) one can meet an inexact interpretation of the well-known Schwinger formulas describing pair-creation from vacuum by a constant electric field [2]. Such an interpretation may lead to incorrect results for some field strengths, as noted in [36].…”

“…Then the probabilities P v for vacuum to remain vacuum are found, for both quarks and gluons, from relation (56). However, formulas for parton production rates derived in [12] hold only in the approximation 2 Im S quark p ⊥ ≪ 1 and 2 Im S gluon p ⊥ ≪ 1 by virtue of the arguments we presented at the end of subsection 3.2. To obtain exact results, we can use the following line of reasoning.…”

“…. , 8) along the x 3 -axis, see [12]. In this work, the imaginary parts of one-loop effective actions for quarks S quark and gluons S gluon were calculated via gauge-invariant p ⊥ distributions S quark p ⊥ and S gluon p ⊥ respectively.…”

“…Considerable attention has been recently focused on a non-perturbative parton production from vacuum by a classical chromoelectric field of SU(3) [12,13] and SU (2) [14] in the framework of a modern version of the known chromoelectric flux tube model [15], the latter being an effective model for the confinement of quarks in QCD (previously the pair creation by a constant field has been calculated for SU (2) in [16] and for SU (3) in [17]). The model ensures a very good description of the phenomenology of hadron jets in high-energy e + − e − and p −p collision experiments (for further development of the basic model and phenomenological applications, see, e.g., review [18]).…”

Transient field fluctuations effects ind+Auand Au+Au collisions atsNN=200Pop1, Gyulassy2, Barrette3 et al. 2007Phys. Rev. C21090View full textAdd to dashboardCite

“…A sizable rate for spontaneous pair production requires "strong electric fields", and |e eff E|/m 2 > 1. Recently, non-perturbative gluon and quarkantiquark pair production from a constant chromoelectric field with arbitrary color index via vacuum polarization have been also investigated in a QCD formalism [47]. Although the p T dependence of the rate of production is different because of the presence of the nontrivial color generators in QCD, the integration over p T , reproduced also Schwinger's result for total production rate used here to estimate the suppression of heavier flavors.…”