“School of Particles”
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| Paper IPM / Particles / 15786 |
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The distribution of flow harmonics in heavy ion experiment can be characterized by standardized cumulants.
We first model the ellipticity and power parameters of the elliptic-power distribution by employing MC-Glauber model.
Then we use the elliptic-power distribution together with the hydrodynamic linear response approximation to study the two dimensional standardized cumulants of elliptic and triangular flow (v2 and v3) distribution. For the second harmonic, it turns out that finding two dimensional cumulants in terms of 2q-particle correlation functions c2{2q} is limited to the skewness. We also show that c3{2}, c3{4}, and c3{6}, are related to the second, fourth, and sixth standardized cumulants of the v3 distribution, respectively. The cumulant cn{2q} can be also written in terms of vn{2q}. Specifically, −(v3{4}/v3{2})4 turns out to be the kurtosis of the v3 event-by-event fluctuation distribution. We introduce a new parametrization for the distribution p(v3) with v3{2}, kurtosis and sixth-order standardized cumulant being its free parameters. Compared to the Gaussian distribution, it indicates a more accurate fit with experimental results. Finally, we compare the kurtosis obtained from simulation with that of extracted from experimental data for the v3 distribution.
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