Kinetic approach to a relativistic BEC with inelastic processes

The phenomenon of Bose-Einstein condensation is investigated in the context of the Color-Glass-Condensate description of the initial state of ultrarelativistic heavy-ion collisions. For the first time, in this paper we study the influence of particle-number changing $2 \leftrightarrow 3$ processes on the transient formation of a Bose-Einstein Condensate within an isotropic system of scalar bosons by including $2 \leftrightarrow 3$ interactions of massive bosons with constant and isotropic cross sections, following a Boltzmann equation. The one-particle distribution function is decomposed in a condensate part and a non-zero momentum part of excited modes, leading to coupled integro-differential equations for the time evolution of the condensate and phase-space distribution function, which are then solved numerically. Our simulations converge to the expected equilibrium state, and only for $\sigma_{23}/\sigma_{22} \ll 1$ we find that a Bose-Einstein condensate emerges and decays within a finite lifetime in contrast to the case where only binary scattering processes are taken into account, and the condensate is stable due to particle-number conservation. Our calculations demonstrate that Bose-Einstein Condensates in the very early stage of heavy-ion collisions are highly unlikely, if inelastic collisions are significantly participating in the dynamical gluonic evolution.