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onperturbative Dynamics of an Expanding Flux-Tube in the Theory of Heavy Ion Collisions¶ A. V. Friesena, b and S. A. Smolyanskyb a

Joint Institute for Nuclear Research, 141980 Dubna, Russia Theoretical and Mathematical Physics Department, Saratov State University, 410026 Saratov, Russia Abstract—The considered variant of the flux-tube model is based on the joint action of the same mechanisms of the vacuum particle creation as the standard Schwinger mechanism and the Casimir effect. It is assumed that pre-equilibrium quark–gluon plasma (QGP) is created in ultrarelativistic heavy-ion collision. According to the considered model, these two mechanisms act at different time scales and lead to qualitatively different momentum distributions. PACS numbers: 25.75.-q, 12.38.Mh DOI: 10.1134/S1063779608070241 b

1. INTRODUCTION The present model deals with the early stage QGP formation in the heavy-ion collision. This stage is characterized by vacuum polarization effects caused by a small initial size of the system. There are two mechanisms of secondary QGP formation: the standard Schwinger-like mechanism (SM) [1, 2] and the dynamical Casimir effect (CM) (e.g., [3, 4], where this effect is rated in application to the photon generation into the cavities with moving boundaries). It was shown in works [5] that CM is effective at the most early stage of the expanding process, when the gluon field is rather weak in order to make SM play some appreciable role. In the present work, the kinetic equations (KE) set for description of the pair creation is formulated within the framework of the simplest scalar field model and impenetrable boundary conditions. The initial value problem is discussed too.

A further stage of the collision is characterized by the QGP creation and expansion. It is assumed that the cylinder has plane impenetrable external boundaries devoid of diffuse layers. This assumption brings choice of the periodical basis functions (see Eq. (2)) and to CM of vacuum particle creation. The strong quasi-classical gluon fields emerging between the flying away primordial partons lead to generation of the secondary sea partons by means of SM of vacuum particle creation [2]. To derive KE the method of work [6] is used, where KE is for the vacuum creation of the scalar bosons in an expanding flux tube in the presence of a strong electric 3 field acting along the tube: E(t) = (0, 0, E(t) = – A˙ (t)) is derived. The oscillator representation [6] is based on the standard decomposition of the field functions and substitution

=

2. KINETIC EQUATIONS The main assumptions of the model are the follows. The system of two identical colliding ions is considered in their center-of-mass frame. Before the collision both ions can be represented as Lorentz-contracted disks – 1/2 with the thickness L0 = 2r0A1/3mN S NN , where r0 is the

2

ωp =

m +p 2

ωp ( t )

2

(1)

3 2

3

m + p⊥ + [ p – e A ] ,

where p3 is defined by the discrete set p3 = πn/L with integer n ≥ 0. In connection with their presence in the system of boundaries, the symmetric