Multiparticle azimuthal cumulants from transverse momentum conservation and collective flow

TL;DR

This paper derives formulas for multiparticle azimuthal cumulants considering transverse momentum conservation and collective flow, revealing how their interplay affects sign changes and can probe collectivity and proton substructure in small systems.

Contribution

It provides a theoretical framework for understanding azimuthal cumulants incorporating TMC and flow effects, highlighting their impact on sign changes and potential to study small system collectivity.

Findings

TMC causes specific sign patterns in cumulants.

Interplay between TMC and flow can change cumulant signs.

Sign changes in cumulants can probe collectivity and proton substructure.

Abstract

We calculate the $n$th order of $2k$-particle azimuthal cumulants $c_n\{2k\}$ based on transverse momentum conservation (TMC) and collective flow $v_n$(n=2,3). We demonstrate that the TMC effect only leads to a nonzero $c_n\{2k\}$ with the sign of $(-1)^{nk}$ and the magnitude inversely proportional to $(N-2k)^{nk}$. The interplay between TMC and collective flow can change the signs of $c_2\{4\}$, $c_3\{2\}$ and $c_3\{4\}$ at some values of multiplicity $N$, which could provide a good probe to study the onset of collectivity and search for the substructure of proton in small colliding systems.