How transverse momentum conservation breaks azimuthal correlation factorization

Jia-Lin Pei; Guo-Liang Ma; Adam Bzdak

paper

How transverse momentum conservation breaks azimuthal correlation factorization

arXiv:2601.19475

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 $(- 1)^{n + 1}$ , 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.

17 pages, 9 figures