Creation of boson and fermion pairs in strong fields

We analyze a quantum kinetic equation describing both boson and fermion pair production. We explore the solution of the kinetic equation in its Markovian limit. The numerical study shows an enhancement (bosons) or a suppression (fermions) of the pair creation rate according to their quantum statistics. The modification of the time evolution of the distribution function is small but for strong fields more pronounced than for weak fields. PACS: 12.38.Mh, 05.60.+w, 25.75.Dw The pre-equilibrium evolution of the quark-gluon plasma, believed to be created in an ultrarelativistic heavy-ion collision, is described by means of a transport equation that can be used to explore dynamical properties in the plasma phase. The formation of the QGP is assumed to proceed via the creation of a strong chromoelectric field in the region between the two receding nuclei after the collision. The field subsequently decays by emitting quark-antiquark pairs according to the nonperturbative tunneling process of the Schwinger mechanism. The process of parton pair production within the Schwinger mechanism [1] has been addressed by many authors in recent years [2], with the back reaction scenario [3] also considered. While these studies have been very useful in exploring new phenomena such as plasma oscillations, the phenomenological approaches suffer from the lack of a derivation of a source term within a kinetic theory. Indeed such a consistent field theoretical treatment leads to a modified source term providing a non-Markovian evolution of the distribution function. This result was first obtained by Rau [4] for a constant electric field. A generalized treatment allowing for a time dependent field was demonstrated in Ref. [5]. A systematic numerical study of the time structure of such a source term was provided in Ref. [6] for the case of the creation of boson pairs. In Ref. [5], using a field theoretical treatment we have derived a kinetic equation characterized by the following properties: (i) it has non-Markovian character, (ii) the distribution function of the produced particles has a non-trivial momentum dependence and (iii) due to the statistical factor [1 ± 2f±( ¯ P , t)] the production is modified according to the quantum statistics of the created pairs. The properties of the source term itself such as the momentum dependence and the time structure have been studied in Ref. [5] for a constant and a time dependent field. However, a numerical analysis of the evolution of the distribution function was not provided. In this paper we explore the solution of the kinetic equation in the Markovian limit in order to compare fermion and boson pair production. Using a simple field-theoretical model of charged fermions in an external, homogeneous, timedependent field characterized by the vector potential Aµ = (0,0,0, A(t)) with A(t) = A3(t) and the resulting electric field E(t) = E3(t) = − u A(t) = −dA(t)/dt, we obtained [5] the kinetic equation for the distribution function f± = f±( ¯ P , t)