Flow analysis with cumulants: direct calculations

TL;DR

This paper tackles biases and computational challenges in measuring anisotropic flow via multi-particle cumulants. It introduces a direct, exact cumulant calculation based on moments of $Q$-vectors, eliminating harmonic interference and interpolation biases inherent in generating-function approaches. The method preserves linear scaling with multiplicity and cleanly accommodates detector acceptance effects, enabling robust estimates of both reference and differential flow. Extensive simulations validate the approach up to $8^{\text{th}}$ order and demonstrate its practical applicability to real data analysis.

Abstract

Anisotropic flow measurements in heavy-ion collisions provide important information on the properties of hot and dense matter. These measurements are based on analysis of azimuthal correlations and might be biased by contributions from correlations that are not related to the initial geometry, so called non-flow. To improve anisotropic flow measurements advanced methods based on multi-particle correlations (cumulants) have been developed to suppress non-flow contribution. These multi-particle correlations can be calculated by looping over all possible multiplets, however this quickly becomes prohibitively CPU intensive. Therefore, the most used technique for cumulant calculations is based on generating functions. This method involves approximations, and has its own biases, which complicates the interpretation of the results. In this paper we present a new exact method for direct calculations of multi-particle cumulants using moments of the flow vectors.

Figures (6)

• Figure 1: Schematic view of a non-central nucleus-nucleus collision in the transverse plane.
• Figure 2: Elliptic flow extracted by different methods for $10^5$ simulated events with multiplicity $M=500$, $v_2=0.05$ and at the same time $v_4=0.1$.
• Figure 3: a) The azimuthal distribution of accepted particles. b) Extracted elliptic flow accounting for acceptance effects, closed markers, and without, open markers. c) Extracted elliptic flow accounting for acceptance effects in different methods.
• Figure 4: Reference flow extracted from particles labeled as RFPs (pions in Therminator)
• Figure 5: Differential flow extracted for particles labeled as POIs from Therminator events (in this example we used protons). The open circles denote $2^{\rm nd}$ order estimate (Eq. (\ref{['diffFlow2nd:Result']})) and closed squares denote $4^{\rm th}$ order estimate (Eq. (\ref{['diffFlow4th:Result']})).