Azimuthal asymmetries and the emergence of "collectivity" from multi-particle correlations in high-energy pA collisions

TL;DR

This work analyzes the origin of azimuthal anisotropies in high-energy pA collisions within a dipole scattering framework, attributing $\cos 2\phi$ modulations to anisotropic fluctuations of the target's saturation momentum organized into domains. By modeling domain structure with correlation length $\xi$ and anisotropy amplitude $\cal A$, the authors derive analytic expressions for the two- and four-particle cumulants: $c_2\{2\} = \frac{1}{N_D}\left({\cal A}^2 + \frac{1}{4(N_c^2-1)}\right)$ and $c_2\{4\} = -\frac{1}{N_D^3}\left({\cal A}^4 - \frac{1}{4(N_c^2-1)^3}\right)$. The fully connected four-point contribution is shown to be positive, implying a sign change in $c_2\{4\}$ when $\cal A$ is of order $N_c^{-3/2}$, signaling a transition toward dominance by fully disconnected multi-particle correlations. The discussion links these results to the emergence of collectivity in high-multiplicity events, offering qualitative insight into the LHC pA data and highlighting the role of domain-based small-$x$ QCD dynamics. The work also notes the need to understand multiplicity bias and hard-soft decorrelations within this framework.

Abstract

We show how angular asymmetries $\sim\cos 2φ$ can arise in dipole scattering at high energies. We illustrate the effects due to anisotropic fluctuations of the saturation momentum of the target with a finite correlation length in the transverse impact parameter plane, i.e.\ from a domain-like structure. We compute the two-particle azimuthal cumulant in this model including both one-particle factorizable as well as genuine two-particle non-factorizable contributions to the two-particle cross section. We also compute the full BBGKY hierarchy for the four-particle azimuthal cumulant and find that only the fully factorizable contribution to $c_2\{4\}$ is negative while all contributions from genuine two, three and four-particle correlations are positive. Our results may provide some qualitative insight into the origin of azimuthal asymmetries in p+Pb collisions at the LHC which reveal a change of sign of $c_2\{4\}$ in high-multiplicity events.