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

We study the energy distribution of hard gluons traversing a dense quark-gluon plasma by comparing various transverse momentum broadening rates q<^>(t), using a probabilistic perturbative approach. These results were applied to address the thermalization problem in heavy ion collisions. Within the weak coupling model, thermalization follows a "bottom-up" process: early-formed high-energy partons emit low-energy gluons, leading to their equilibrium formation, creating a thermal bath that facilitates equilibrium in the high-energy sector. Under this scenario, we model the time dependencies of q<^>(t) as a power-law q<^>(t) similar to t(n), and assess the impact of n on the distribution of hard gluons passing through the medium.