Hard gluon evolution in warming medium

Abstract

We describe the energy distribution of hard gluons travelling through a dense quark–gluon plasma whose temperature increases linearly with time, within a probabilistic perturbative approach. The results were applied to the thermalization problem in heavy ion collisions. In the weak coupling picture this thermalization occurs from “the bottom up”: high energy partons, formed early in the collision, radiate low energy gluons which then proceed to equilibrate among themselves, forming a thermal bath that brings the high energy sector to equilibrium. We see that, in this scenario, the dynamic we describe must set in around $$t \sim 0.5$$ t ∼ 0.5 fm/c after the collision in order to reach a fully thermalized state at $$t \sim 1$$ t ∼ 1 fm/c. We then look at the entropy density and average temperature of the soft thermal bath, as the system approaches (local) thermal equilibrium.

Evolution of hard gluons in a medium with q^(t)∼tn and the thermalization problem

“…Also, $$$ {\hat{q}}_o $$$ may be treated as another free parameter in the theory or it may be set by imposing $$$ {\hat{q}}_o{t}_o\approx {Q}_s^2 $$$, as in Caucal et al (2020). In order to keep the number of degrees of freedom to a minimum, we shall take $$$ {\hat{q}}_o={Q}_s^2/{t}_o $$$ in what follows, with $$$ {t}_o\approx 0.5 $$$ fm/c (Ben & Machado 2022b).…”

“…Subsequent studies explored its application to an expanding medium (Adhya et al 2020; Caucal et al 2020), either through a modified emission rate or by equating the expanding medium to an effective static one. We employed these findings in the thermalization problem in previous papers (Ben & Machado 2022a, 2022b). In this work, we apply the formalism established in Blaizot et al (2013, 2014) and Caucal et al (2020) to analyze hard gluons traveling within a homogeneous QGP, considering $$$ \hat{q}(t)\sim {t}^n $$$, and we compare the impact of various $$$ n $$$ values on the energy distribution.…”