Bose–Einstein condensation and thermalization of the quark–gluon plasma

Abstract

In ultra-relativistic heavy ion collisions, the matter formed shortly after the collision is a dense, out of equilibrium, system of gluons characterized by a semi-hard momentum scale Qs. Simple power counting arguments indicate that this system is over-occupied: the gluon occupation number is parametrically large when compared to a system in thermal equilibrium with the same energy density. On short time scales, soft elastic scatterings tend to drive the system towards the formation of a Bose-Einstein condensate that contains a large fraction of the gluons while contributing little to the energy density. The lifetime and existence of this condensate depends on whether inelastic processes, that occur on the same time scale as the elastic ones, preferably increase or decrease the number of gluons. During this overpopulated stage, and all the way to thermalization, the system behaves as a strongly interacting fluid, even though the elementary coupling constant is small. We argue that while complete isotropization may never be reached, the system may yet evolve for a long time with a fixed anisotropy between average longitudinal and transverse momenta.

Anomalous transport effects and possible environmental symmetry ‘violation’ in heavy-ion collisions

“…However, recent analysis in [67] appears to suggest that even with unrealistically large conductivity the magnetic field would still drop fairly quickly, thus one may not expect a lifetime of such fields to be beyond ∼ 1fm/c time. A conclusive answer may require more detailed understanding of the pre-thermal evolution [73], in particular the electric conductivity in such highly off-equilibrium partonic system. A closely related issue is how the field-induced effects should evolve with the collisional beam energy.…”

The extraordinary glow

“…As pointed out in [19], such high occupation coherently amplifies scattering and changes usual power counting of scattering rate: the resulting collision term from the 2 ↔ 2 gluon scattering process will scale as ∼ α 2 s f 2 ∼ô(1) despite smallish α s . This is a natural consequence of the essential Bose enhancement factor (1 + f ) which would scale as f in the dense regime while scale as 1 in the dilute regime.…”

“…This may be true in the dilute regime (close to the Boltzmann limit), however may not be the accurate picture when the system under consideration is in the highly overpopulated regime with f ∼ 1/α s . As shown in a number of recent kinetic studies [19,20,21,22,23,24], the elastic scatterings with highly overpopulated initial conditions can lead to order ∼ α 0 s evolution and develop strong infrared cascade with the Bose enhancement, and in fact may even induce a dynamical Bose-Einstein Condensation. (In passing let us mention that there have also been lots of developments in understanding the evolution of overpopulated glasma with different approaches, see e.g.…”

“…A novel finding [19,20], hitherto unrealized, is that a system with such initial condition is highly overpopulated: that is, the gluon occupation number is parametrically large when compared to a system in thermal equilibrium with the same energy density. To illustrate this point, consider the energy and particle number densities with the initial distribution (1), we have…”

High temperature Bose-Einstein condensation

“…It can be due to fast expansion and overcooling of the QGP [12,13], or due to gluon condensation in Color Glass Condensate [14], and subsequent hadronization of the low p T gluons into low p T pions [15]. The non-equilibrium hadronization can explain the measured particle ratios [8], and also the spectra [16,17] very well.…”