Anisotropic fluctuations of angular momentum of heavy quarks in the Glasma

We study the evolution of the angular momentum of the heavy quarks in the very early stage of high energy nuclear collisions, in which the background is made of evolving Glasma fields. Given the novelty of the problem, we limit ourselves to the use of toy heavy quarks with a large, unphysical mass, in order to implement the kinetic equations for the angular momentum in the non-relativistic limit. We find that as a consequence of the anisotropy of the background fields, angular momentum fluctuations are also anisotropic: we understand this in simple terms relating the fluctuations of the angular momentum, $L$, to those of linear momentum. While orbital angular momentum diffuses and develops substantial fluctuations and anisotropies, the spin does not. Hence, we can identify the fluctuations of $L$ with those of the total angular momentum $J=L + S$. Therefore, our study suggests that the total angular momentum of the heavy quarks in the early stage of high energy nuclear collisions will present anisotropic fluctuations.