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Explaining higher-order correlations between elliptic and triangular flow

Mubarak Alqahtani, Jean-Yves Ollitrault

Abstract

The ALICE Collaboration has analyzed a number of cumulants mixing elliptic flow ($v_2$) and triangular flow ($v_3$), involving up to $8$ particles, in Pb+Pb collisions at the LHC. We unravel an unexpected simplicity in these complex mathematical quantities for collisions at fixed impact parameter. We show that as one increases the order in $v_2$, for a given order in $v_3$, the changes in the cumulants are solely determined by the mean elliptic flow in the reaction plane, which originates from the almond-shaped geometry of the overlap area between the colliding nuclei. We derive simple analytic relations between cumulants of different orders on this basis. Some of these relations are in reasonable agreement with existing data. We postulate that agreement will be much improved if the analysis is repeated with a finer centrality binning and a larger pseudorapidity acceptance.

Explaining higher-order correlations between elliptic and triangular flow

Abstract

The ALICE Collaboration has analyzed a number of cumulants mixing elliptic flow () and triangular flow (), involving up to particles, in Pb+Pb collisions at the LHC. We unravel an unexpected simplicity in these complex mathematical quantities for collisions at fixed impact parameter. We show that as one increases the order in , for a given order in , the changes in the cumulants are solely determined by the mean elliptic flow in the reaction plane, which originates from the almond-shaped geometry of the overlap area between the colliding nuclei. We derive simple analytic relations between cumulants of different orders on this basis. Some of these relations are in reasonable agreement with existing data. We postulate that agreement will be much improved if the analysis is repeated with a finer centrality binning and a larger pseudorapidity acceptance.

Paper Structure

This paper contains 9 sections, 22 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Cumulants of flow fluctuations in the laboratory frame
  3. Cumulants of flow fluctuations in the intrinsic frame
  4. Definitions and general properties
  5. Power-counting scheme
  6. Relations between experimental cumulants and intrinsic cumulants
  7. Relations between cumulants of different orders
  8. Conclusions
  9. Moments and cumulants of $v_2$

Figures (5)

  • Figure 1: Comparison between ALICE ALICE:2021adw and ATLAS ATLAS:2019peb data on $nMHC(v_2^2,v_3^2)$ in Pb+Pb collisions at 5.02 TeV per nucleon pair, as a function of the collision centrality. ATLAS denotes this quantity by $nsc_{2,3}\{4\}$.
  • Figure 2: Mixed harmonic cumulants as a function of centrality for Pb+Pb collisions at 5.02 TeV per nucleon pair. The normalized cumulants (\ref{['defnMHC']}) are taken from Ref. ALICE:2021adw, and the moments in the denominator are evaluated using earlier ALICE data ALICE:2016ccg and formulas in Appendix \ref{['s:v2cumulants']}. For the negative cumulants, we change the sign before taking the logarithm. $MHC(v_2^4,v_3^4)$ and $MHC(v_2^2,v_3^6)$ are positive for the most central bins, and the three corresponding data points are circled.
  • Figure 3: Schematic representation of two collision events with the same impact parameter seen in the laboratory frame and in the intrinsic frame. The dots in the overlap area correspond to the positions of participants nucleons at the time of impact, which takes a snapshot of the nuclear wavefunction.
  • Figure 4: Ratios in Eqs. (\ref{['ratios0']}) and (\ref{['ratios1']}). Symbols are ALICE data, where the mixed cumulants are taken from Ref. ALICE:2021adw and $v_2\{4\}$ from Ref. ALICE:2016ccg, as a function of the collision centrality in Pb+Pb collisions at 5.02 TeV per nucleon pair. Horizontal lines are our theory predictions.
  • Figure 5: Same as Fig. \ref{['fig:ratios']} for the ratios Eqs. (\ref{['ratios3']}) and (\ref{['ratios4']}).