Multifractal analysis of heavy-ion collisions at RHIC and LHC energies

An extensive analysis of HYDJET++ generated heavy-ion collision data at collider energies is carried out using Takagi moment method based multifractal analysis approach, to search for the presence of local density fluctuations. We report first analysis on multifractality in Au-Au collisions for the RHIC energies, s N N = 14.5 to 200 GeV and in Pb-Pb collisions at LHC energies, s N N = 2.76 to 5.02 TeV in two-dimensional ( η − ϕ ) phase-space. The generalized dimension D q for different orders q at different centralities have been calculated using the methodology proposed by Takagi. The calculated D q values are found to exhibit collision energy as well as centrality dependent behaviour and analysis suggests the multifractal behaviour of charged particle spectra at collider energies. The linear dependence of the D q values as a function of ln q ( q − 1 ) favours the multifractal Bernoulli representation and the values of multifractal specific heat, c, have been extracted from the D q values to perform a comparative analysis with the available experimental data and other model results at collider energies. A slowly decreasing trend of the c values with increasing beam energy is observed for nuclear collisions at collider energies. In addition to this, the centrality dependent behaviour of the HYDJET++ calculated ’c’ values is observed for A-A collisions at collider energies. Further, Ginzberg-Landau (GL) theory framework is utilised here to analyse the dynamics of the HYDJET++ simulated A-A collisions at considered RHIC and LHC energies. A comparative analysis of the HYDJET++ calculated value of the critical exponent ’ ν ’, with other model calculations and with the reported experimental measurements is also presented. The ’ ν ’ values calculated in the present analysis exhibit approximately a constant value less than the value predicted by GL thoery for the considered RHIC and LHC energies, whereas it is quite close to 1 at LHC energies, agreeing well with the value predicted by 2D Ising model.