How transverse momentum conservation breaks azimuthal correlation factorization

摘要: The breakdown of azimuthal two-particle correlation factorization, quantified by the ratios r₂ and r₃, serves as a sensitive probe of transverse-momentum-dependent flow fluctuations. While hydrodynamic models predict r₃≤1, experimental data from CMS in p-Pb collisions exhibit r₃ > 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 r2 and r3. 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 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.