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.

Figures (6)

• Figure 1: Bayesian posterior probability distributions of $v_2$, $v_3$, and $r$ ($r = p^2 / \langle p^2 \rangle_F$) parameters from MCMC sampling. The left pairplot corresponds to $p$+$p$ collisions, the right to $p$+Pb collisions. Diagonal elements represent marginal posterior distributions via kernel density estimation, and off-diagonal elements show joint posterior distributions as scatter plots, revealing inter-parameter dependencies.
• Figure 2: Comparison between Bayesian inference results and ATLAS experimental data for cumulants and symmetric cumulants. Data points represent experimental measurements, while curves show analytical results obtained by substituting Bayesian-inferred parameters into the TMC formula. Red symbols and curves correspond to the $p$+$p$ system, and blue to the $p$+Pb system.
• Figure 3: Comparison of cumulants and symmetric cumulants from Bayesian inference with ATLAS experimental measurements. Symbols denote experimental measurements, and curves show TMC results using Bayesian-inferred parameters that follow a power-law scaling with $N_\text{ch}$. Red (blue) corresponds to $p$+$p$ ($p$+Pb) collisions.
• Figure 4: Comparison of the $v_2$ and $v_3$ values extracted from cumulants with experimental data, and of the parameter $r$ with model calculations, using PYTHIA 8 for $p$+$p$ and AMPT for $p$+Pb. Red and blue symbols/lines represent the $p$+$p$ and $p$+Pb systems, respectively.
• Figure 5: Comparison between the Bayesian analytical results and experimental data for $c_2\{4\}$ and $c_3\{2\}$, decomposed into different physical contributions. The top row shows the $p$+$p$ system, and the bottom row the $p$+Pb system. The yellow, green, and purple dashed lines represent the contributions from pure flow, pure TMC, and their interplay, respectively.