Reexamination for the calculation of elliptic flow and other fourier harmonics

TL;DR

This paper revisits the calculation method of elliptic flow and Fourier harmonics in particle physics, emphasizing the importance of event-wise averaging over particle-wise averaging to account for multiplicity fluctuations.

Contribution

It proposes a revised calculation approach for Fourier harmonics that improves accuracy by considering event-wise averages instead of particle-wise averages.

Findings

Event-wise averaging yields more accurate Fourier harmonic calculations.

Particle multiplicity fluctuations significantly affect harmonic measurements.

Revised method improves consistency in flow analysis across different centrality bins.

Abstract

We have argued that the azimuthal symmetry and asymmetry components in fourier expansion of particle momentum azimuthal distribution, $v_n$ (n=0, 1, 2, ...), should be calculated as an average of $cos(n\phi)$ first over particles in an event and then over events (event-wise average) rather than "an average over all particles in all events" (particle-wise average). In case of large centrality (multiplicity) bin the particle-wise average is not accurate because the influence (fluctuation) of particle multiplicity was not taken into account.