Non-Bessel-Gaussianity and Flow Harmonic Fine-Splitting

Hadi Mehrabpour; Seyed Farid Taghavi

doi:10.1140/epjc/s10052-019-6549-2

paper

Non-Bessel-Gaussianity and Flow Harmonic Fine-Splitting

arXiv:1805.04695 · doi:10.1140/epjc/s10052-019-6549-2

Abstract

Both collision geometry and event-by-event fluctuations are encoded in the experimentally observed flow harmonic distribution $p (v_{n})$ and $2 k$ -particle cumulants $c_{n} {2 k}$ . In the present study, we systematically connect these observables to each other by employing Gram-Charlier A series. We quantify the deviation of $p (v_{n})$ from Bessel-Gaussianity in terms of flow harmonic fine-splitting. Subsequently, we show that the corrected Bessel-Gaussian distribution can fit the simulated data better than the Bessel-Gaussian distribution in the more peripheral collisions. Inspired by Gram-Charlier A series, we introduce a new set of cumulants $q_{n} {2 k}$ that are more natural to study distributions near Bessel-Gaussian. These new cumulants are obtained from $c_{n} {2 k}$ where the collision geometry effect is extracted from it. By exploiting $q_{2} {2 k}$ , we introduce a new set of estimators for averaged ellipticity $v ˉ_{2}$ which are more accurate compared to $v_{2} {2 k}$ for $k > 1$ . As another application of $q_{2} {2 k}$ , we show we are able to restrict the phase space of $v_{2} {4}$ , $v_{2} {6}$ and $v_{2} {8}$ by demanding the consistency of $v ˉ_{2}$ and $v_{2} {2 k}$ with $q_{2} {2 k}$ equation. The allowed phase space is a region such that $v_{2} {4} - v_{2} {6} ≳ 0$ and $12 v_{2} {6} - 11 v_{2} {8} - v_{2} {4} ≳ 0$ , which is compatible with the experimental observations.

arXiv comment24 pages; 9 figures; v2: published version; minor revision of the text

Non-Bessel-Gaussianity and Flow Harmonic Fine-Splitting

Abstract

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