Bayesian extraction of TMC-free collectivity in proton-proton and proton-nucleus 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 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 TMC-free collectivity in small systems. Our analysis indicates that while the TMC-free 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 extracted $v_2$ 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 TMC-free flow in $p$+$p$ collisions, due to competing contributions from TMC effects. This establishes a robust and data-driven framework, enabling a quantitatively controlled interpretation of collective signals and opening a new avenue for understanding the origin of collectivity in small collision systems.

16 pages, 6 figures, accepted for publication in SCIENCE CHINA Physics, Mechanics & Astronomy