Bayesian extraction of TMC-free collectivity in p+p and p+Pb collisions at the LHC

Abstract: A central challenge in understanding the origin of collective flow-like signatures in small collision systems calls for a reliable method to disentangle genuine collective flow from substantial background correlations, especially those arising from transverse momentum conservation (TMC). A Bayesian inference framework is developed to integrate TMC calculations with the LHC-ATLAS data on long-range multiparticle azimuthal correlation observables, thereby extracting genuine collective flow in small systems. Our analysis indicates that while the genuine elliptic and triangular flow ($v_{2}$ and $v_{3}$) are similar, the $p$+$p$ and $p$+Pb systems exhibit distinct TMC backgrounds, TMC-flow interplay, and $v_{2}$--$v_{3}$ correlations. We demonstrate that the genuine $v_{2}$ and $v_{3}$ are well described by the measured four-particle $v_2{4}$ and two-particle $v_3{2}$ in $p$+Pb collisions, whereas these measurements systematically underestimate the genuine flow in $p$+$p$ collisions, due to competing contributions from TMC effects. This establishes a robust and data-driven approach, providing renewed theoretical insight into collective behavior free from TMC contamination in small collision systems.