Skewness of the elliptic flow distribution in $\sqrt{s_{_{\mathrm{NN}}}}$ = 5.02~TeV PbPb collisions from HYDJET++ model

The elliptic flow ($v_{2}$) event-by-event fluctuations in PbPb collisions at 5.02~TeV are analyzed within the HYDJET++ model. Using the multi-particle, so called Q-cumulant method, $v_{2}\{2\}$, $v_{2}\{4\}$, $v_{2}\{6\}$ and $v_{2}\{8\}$ are calculated and used to study their ratios and to construct skewness ($\gamma^{exp}_{1}$) as a measure of the asymmetry of the elliptic flow distribution. Additionally, in order to check if there is a hydrodynamics nature in the elliptic collectivity generated by the HYDJET++ model, the ratio of $v_{2}\{6\} - v_{2}\{8\}$ and $v_{2}\{4\} - v_{2}\{6\}$ distribution is calculated. The analysis is performed as a function of the collision centrality. In order to check the HYDJET++ model responses, the results of this analysis are compared to the corresponding experimental measurements by CMS. A good qualitative and rather good quantitative agreement is found.

This anisotropy is converted into momentum space by the hydrodynamic expansion. The momentum anisotropy can be characterized by a Fourier expansion of the emitted hadron yield distribution in azimuthal angle, φ, [16][17][18] where Fourier coefficients, v n , represent magnitude of the azimuthal anisotropy measured with respect to the corresponding flow symmetry plane angle, Φ n . The flow symmetry plane is determined by the geometry of the participant nucleons and can be reconstructed from the emitted particles themselves. Because of fluctuations in the initial spatial geometry, all orders of Fourier harmonics are present. The second order Fourier coefficient, v 2 , is called elliptic flow, while the angle Φ 2 corresponds to the flow symmetry plane which is determined by the beam direction and the shorter axis of the roughly lenticular shape of the nuclear overlap region.
Another experimental method to determine the v n coefficients is multi-particle cumulant analysis which uses the Q-cumulant method [19]. The multi-particle cumulant technique has the advantage of suppressing short-range correlations arising from jets and resonance decays and revealing the collective nature of the observed azimuthal correlations. The two-, four-, six-, and eight-particle azimuthal correlations are calculated as: where ... denotes averaging over all particle multiplets and over all events from a given centrality 1 class, n is harmonic order and φ i (i = 1, ..., 8) are the azimuthal angles of particles from a given particle multiplet. The corresponding multiparticle cumulants c n {2k} (k = 1, ..., 4) are then given as [19]: Finally, the Fourier coefficients v n are connected to the above defined multi-particle cumulants through the following relations The unitless standardized skewness, γ exp 1 , of the event-by-event elliptic flow magnitude distribution is a measure of the asymmetry about its mean. This standardized skewness can be estimated using the cumulant elliptic flow harmonics defined as in Ref. [20] γ exp In the case where the event-by-event elliptic flow magnitude fluctuations stem from an isotropic Gaussian transverse initial-state energy density profile, the skewness, γ exp 1 becomes equal to zero. But, non-Gaussian fluctuations in the initial-state energy density profile could be present [20], and as a consequence will produce differences in the higher order cumulant v 2 {2k} (k ≥ 2) coefficients. As Eq. (5) is an approximation of the standardised skewness γ 1 defined in [20], it is possible to test its validity through the universal equality given in [20] v In this paper, we study the skewness of the elliptic flow distribution using the HYD-JET++ model. The basic features of HYDJET++ model [21] are described in Sect. 2.
Using ancy between them becomes more pronounced going to more peripheral collisions.
As from Fig. 1      is found to be negative with an increasing magnitude as collisions become less central.
The HYDJET++ model qualitatively predicts correct behavior of the skewness centrality dependence, but gives significantly larger magnitude of the γ exp 1 than the experimental result.