Elliptic flow of charm quarks produced in the early stage of pA collisions

Abstract

We investigate the build-up of elliptic flow of charm quarks produced in the early pre-equilibrium stage of high-energy proton--nucleus collisions. The initial stage is modeled within the Color Glass Condensate framework as an evolving glasma, initialized through the McLerran--Venugopalan model. Subnucleonic fluctuations have been implemented as constituent-quark hotspots for both the proton and the nuclear participants. Charm quarks are propagated in the evolving non-Abelian background by solving the relativistic Wong equations for their coordinates, momenta, and color charges. First, we compute the nuclear modification factor of charm quarks, finding a slight migration towards higher $p_T$ states in agreement with previous results in the literature. Then, we focus on the azimuthal anisotropies acquired through the interaction with glasma fields. We find that glasma-induced momentum anisotropies are efficiently transmitted to heavy quarks within $\tau \sim 0.4~\mathrm{fm/c}$, leading to a sizeable charm-quark $v_2$, with a magnitude that increases with the strength of the initial fields and with the number of nuclear participants. Remarkably, we show that the early-stage contribution alone can account for a significant fraction of the experimentally observed $J/\psi$ elliptic flow in p-Pb collisions, indicating that pre-hydrodynamic dynamics can play a non-negligible role in the final-state heavy-flavor collectivity, especially in small systems.