Azimuthal anisotropies in p+Pb collisions from classical Yang-Mills dynamics

TL;DR

This study uses classical Yang-Mills simulations to analyze azimuthal anisotropies in p+Pb collisions, revealing initial state gluon anisotropies and their evolution, which differ from hydrodynamic expectations and depend on collision geometry.

Contribution

It demonstrates that initial state gluon distributions exhibit significant anisotropy and that final state effects generate odd harmonics, providing new insights into the origin of azimuthal anisotropies in small collision systems.

Findings

Gluons have large initial $v_2$; odd harmonics like $v_3$ vanish initially.

Final state evolution generates non-zero $v_3$ and mildly affects $v_2$.

Anisotropies are uncorrelated with global spatial asymmetry and depend on domain size.

Abstract

We compute single and double inclusive gluon distributions in classical Yang-Mills simulations of proton-lead collisions and extract the associated transverse momentum dependent Fourier harmonics $v_2(p_T)$ and $v_3(p_T)$. Gluons have a large $v_2$ in the initial state, while odd harmonics such as $v_3$ vanish identically at the initial time $\tau=0^{+}$. By the time $\tau \lesssim 0.4\,{\rm fm/c}$ final state effects in the classical Yang-Mills evolution generate a non-zero $v_{3}$ and only mildly modify the gluon $v_{2}$. Unlike hydrodynamic flow, these momentum space anisotropies are uncorrelated with the global spatial anisotropy of the collision. A principal ingredient for the generation of $v_2$ and $v_3$ in this framework is the event-by-event breaking of rotational invariance in domains the size of the inverse of the saturation scale $Q_s$. In contrast to our findings in p+Pb collisions Yang-Mills simulations of lead-lead collisions generate much smaller values of $v_{2,3} (p_T)$ and additional collective flow effects are needed to explain experimental data. This is because the locally generated anisotropy due to the breaking of rotational invariance is depleted with the increase in the number of uncorrelated domains.