Event-shape dependence of symmetry plane correlations using the Gaussian estimator in Pb-Pb collisions at the LHC using a multiphase transport model

TL;DR

The paper addresses how symmetry plane correlations (SPCs) in Pb-Pb collisions reflect initial-state geometry and transport properties. It employs AMPT simulations and a Gaussian estimator to quantify SPCs while classifying events by transverse spherocity, enabling an event-shape–dependent analysis. The key finding is that SPCs are enhanced in low-$S_0$ events and exhibit characteristic centrality and harmonic-order patterns that mirror initial-state fluctuations and nonlinear hydrodynamic responses; PPCs show qualitative agreement with SPCs, confirming their link to initial geometry. This approach provides a practical framework to probe higher-order anisotropies, test models, and inform Bayesian analyses of heavy-ion collision dynamics.

Abstract

The study of symmetry plane correlations (SPCs) can be useful in characterizing the direction of the anisotropic emission of produced particles in the final state. The study of SPCs provides an independent method to understand the transport properties of the system formed in heavy-ion collisions. Similar to anisotropic flow coefficients, which are largely influenced by the initial spatial anisotropy, SPCs also depend upon the participant plane correlations measured using the participating nucleons of the collision overlap region. In this paper, SPCs have been studied in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV using the event generator AMPT. In addition to their behaviour with the changing centrality of the collision, their event shape dependence has also been studied for the first time, using the event shape classifier transverse spherocity. The Gaussian estimator has been used to evaluate the correlations, and these have been compared to the participant plane correlations defined in an analogous way to the symmetry plane correlations, and a qualitative match has been found between them. These event-shape differentiated symmetry plane correlations can be used to deduce the presence of higher-order anisotropies in the initial energy distribution, thus giving insight into the initial geometry of the colliding system, among other applications like model development and model testing using Bayesian analyses.

Figures (7)

• Figure 1: Comparison of the centrality dependence of SPCs calculated using various models, including AMPT from the present study, with ALICE measurements in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV ALICE:2024fus. Corresponding measurements from TRENTO, EKRT+hydrodynamics Niemi:2012ajHirvonen:2022xfv, TRENTO+iEBE-VISHNU Bass:1998caBleicher:1999xiSong:2007uxShen:2014vra are taken from Ref. ALICE:2024fus.
• Figure 2: Centrality dependence of symmetry plane correlations of different orders in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV using AMPT.
• Figure 3: Centrality dependence of SPCs (shown in (a), (b), and (c)) among $n=2, 3, 6$ and corresponding PPCs (shown in (d), (e), and (f)) in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV using AMPT. The calculation of SPCs considers the charged hadrons with $0.2<p_{\rm T}<5.0$ GeV/c, $|\eta|<0.8$.
• Figure 4: Comparison of SPC $\langle\cos[6(\psi_2-\psi_3)]\rangle_{\rm GE}$ between that calculated from events in which $v_6$ dominates $v_2$ and $v_3$, and all other events containing at least five charged hadrons with $p_{\rm T}>0.15$ GeV/c.
• Figure 5: Centrality dependence of SPCs (shown in (a), (b), and (c)) for $n=2,4, 6$ and corresponding PPCs (shown in (d), (e), and (f)) in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV using AMPT. The calculation of SPCs considers the charged hadrons with $0.2<p_{\rm T}<5.0$ GeV/c, $|\eta|<0.8$.