How transverse momentum conservation breaks azimuthal correlation factorization

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 $r_3\le 1$, 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 quantifies a dominant non-flow contribution to the factorization ratios $r_n$ in small systems, and demonstrates that this kinematic effect must be subtracted or accounted for before $r_n$ can be used as a reliable probe of genuine flow fluctuations.

20 pages, 13 figures, accepted for publication in Nuclear Science and Technique