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

TL;DR

The paper addresses how the early pre-equilibrium glasma in high-energy pA collisions generates elliptic flow for charm quarks. It combines CGC/MV-based initial conditions with sub-nucleonic hotspots and real-time lattice Yang–Mills evolution, coupling charm quarks through the Wong equations to quantify momentum-space anisotropies. The study finds that glasma-induced $v_2$ is efficiently transmitted to charm quarks by $\tau\sim0.4$ fm/$c$, with larger effects for stronger initial fields and more participants, and shows that this early-stage contribution can account for a significant fraction of the observed $J/\psi$ $v_2$ in p-Pb, highlighting the importance of pre-hydrodynamic dynamics in small systems. These results provide a baseline for heavy-flavor collectivity and motivate further work on the interplay between pre-equilibrium and hydrodynamic stages.

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 $τ\sim 0.4~\mathrm{fm/c}$, 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 $J/ψ$ 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.

Figures (9)

• Figure 1: Thickness functions in fm$^{-2}$ used for the generation of the color charges. In the left panel we show $T_p$ for the proton (corresponding to $N_\mathrm{part}=1$), in the middle panel we show the case $N_\mathrm{part}=8$, corresponding to the average number of participants in pA collisions at the LHC, and in the right panel we show $T_p$ for the case $N_\mathrm{part}=20$.
• Figure 2: Color-electric and color-magnetic fields vs $\tau$ for pA collisions (1-8 collision, upper panel) and AA collisions (wall-wall collision, lower panel).
• Figure 3: Nuclear modification factor $R_{pA}$ defined in \ref{['eq:RpA_definition']}, computed at $\tau=0.4$ fm/c, for several collision systems.
• Figure 4: Elliptic flow $v_2$ of the glasma fields versus $k_T$, computed at $\tau=0.4$ fm/c, for several collision systems.
• Figure 5: Elliptic flow of glasma fields, computed at $\tau=0.4$ fm/c for several collision systems, integrated over the $k_T$ range $[0,12]$ GeV.