How transverse momentum conservation breaks azimuthal correlation factorization

TL;DR

This paper demonstrates that transverse momentum conservation explains the breakdown of azimuthal correlation factorization in small collision systems, aligning with experimental data and revealing a sign rule for flow fluctuation effects.

Contribution

It introduces an analytical framework showing how transverse momentum conservation causes factorization breakdown and predicts a sign pattern for flow fluctuations in small systems.

Findings

Quantitative agreement with CMS p-Pb data for $r_2$ and $r_3$

Identification of a sign rule: $r_n - 1$ follows $(-1)^{n+1}$

Transverse momentum conservation is the key mechanism behind factorization breakdown

Abstract

The breakdown of azimuthal two-particle correlation factorization, quantified by the ratios $r_2$ and $r_3$, serves as a sensitive probe of transverse-momentum-dependent flow fluctuations. While hydrodynamic models predict $r_3 \leq 1$, experimental data from CMS in p-Pb collisions exhibit $r_3 > 1$, presenting a clear puzzle. We show that transverse momentum conservation (TMC) is the key mechanism dictating this factorization breakdown in small systems. We systematically calculate the effect of TMC as a function of the momentum difference between particles across various multiplicity and momentum ranges. Our results are in quantitative agreement with CMS p-Pb data for both $r_2$ and $r_3$. A central finding is a sign rule: under TMC, the deviation $r_n - 1$ follows $\left ( - 1 \right )^{n+1} $, being negative for even and positive for odd harmonic orders $n$. This work establishes an analytical framework to quantify transverse-momentum-dependent flow fluctuations and provides new insights into the origin of collectivity in small colliding systems.