High order cumulants of the azimuthal anisotropy in the dilute-dense limit: Connected graphs

TL;DR

This paper analytically calculates higher order cumulants of azimuthal anisotropy at high transverse momentum in the dilute-dense limit, revealing properties of connected graphs and harmonic behaviors.

Contribution

It provides the first analytical computation of higher order azimuthal cumulants in the dilute-dense limit using the McLerran-Venugopalan model, highlighting properties of connected graphs.

Findings

Absolute values of $v_2 ext{ } ext{harmonics are approximately equal for large orders}

Harmonics with order $2m=4n$ are complex, a property linked to connected graphs

This property persists in the dense-dense limit.

Abstract

We analytically compute higher order cumulants of the azimuthal anisotropy, $c_2\{2m\}$, and corresponding $v_2\{2m\}$ at high transverse momentum in the dilute-dense limit. The dense target is considered in the framework of the McLerran-Venugopolan model. The absolute values of the harmonics $v_2\{2m\}$ of the azimuthal anisotropy are approximately equal, $|v_2\{2m\}| \approx |v_2\{2m'\}| $, for large $m$ and $m'$. However, the harmonics with order $2m=4n$ are complex. We argue that this is a generic property of connected graphs, which remains true in the dense-dense limit.