Decomposition of multi-particle azimuthal correlations in Q-cumulant analysis

The method of Q-cumulants is a powerful tool for studying the fine details of azimuthal anisotropies in high energy nuclear collisions.This paper presents a new method,based on mathematical induction,to evaluate the analytical form of high-order Q-cumulants.The capability of this method is demonstrated via a toy model that uses the elliptic power distribution to simulate the anisotropic emission of particles,quantified in terms of Fourier flow harmonics v_(n).The method can help in studying the large amount of event statistics that can be collected in the future and allow measurements of the very high central moments of the v_(2)distribution.This can,in turn,facilitate progress in understanding the initial geometry,the input to the hydrodynamic calculations of medium expansion in high energy nuclear collisions,and the constraints on it.

Sub-leading flow modes in PbPb collisions at (~sNN)^(1/2) = 2.76 TeV from the HYDJET++ model

Recent LHC results on the appearance of sub-leading flow modes in Pb Pb collisions at 2.76 TeV, related to initial-state fluctuations, are analyzed and interpreted within the HYDJET＋＋ model. Using the newly introduced Principal Component Analysis（PCA） method applied to two-particle azimuthal correlations extracted from the model calculations, the leading and sub-leading flow modes are studied as a function of the transverse momentum（p T） over a wide centrality range. The leading modes of the elliptic（v2^（1）） and triangular（v3^（1）） flow calculated with the HYDJET＋＋ model reproduce rather well the v2 {2} and v3 {2} coefficients measured experimentally using the two-particle correlations. Within the p T 3 Ge V/c range, where hydrodynamics dominates, the sub-leading flow effects are greatest at the highest p T of around 3 Ge V/c. The sub-leading elliptic flow mode（v2^（2））, which corresponds to the n = 2 harmonic, has a small non-zero value and slowly increases from central to peripheral collisions, while the sub-leading triangular flow mode（v3^（2））, which corresponds to the n = 3 harmonic, is even smaller and does not depend on centrality. For n= 2, the relative magnitude of the effect measured with respect to the leading flow mode shows a shallow minimum for semi-central collisions and increases for very central and for peripheral collisions. For the n= 3 case, there is no centrality dependence. The sub-leading flow mode results obtained from the HYDJET＋＋model are in rather good agreement with the experimental measurements of the CMS Collaboration.