The study of strongly intensive observables for $π^{\pm,0}$ in $pp$ collisions at LHC energy in the framework of PYTHIA model

Abstract

The fractal and phase transitional properties of each type of pions (i.e. $π^{\pm,0}$) through one-dimensional $η-$space, at an energy of $\sqrt{s}=13~$TeV, have been studied with the help of the Scaled Factorial Moment (SFM) framework. To generate simulated data sets for $pp$ collisions under the minimum bias (MB) condition at $\sqrt{s}=13~$TeV, we have employed the Monte Carlo-based event simulator PYTHIA. Various parameters such as the Levy index $(μ)$, degree of multifractality $(r)$, anomalous fractal dimension $(d_q)$, multifractal specific heat $(c)$ and critical exponent $(ν)$ have been calculated. To study the Bose Einstein(BE) effect due to identical particles (here pions) we have also derived these parameters for mixed pion pairs (i.e. $\{π^{+},π^{-}\}$, $\{π^{+},π^{0}\}$ and $\{π^{-},π^{0}\}$) and we find that the effects of identical particles weakened for the mixture with respect to the individual distributions. The quest for the quark-hadron phase transition has also been conducted within the framework of the Ginzburg-Landau (GL) theory of second-order phase transition. Analysis revealed that for PYTHIA-generated MB events, there is a clear indication of the quark-hadron phase transition according to the GL theory. Furthermore, the values of the multifractal specific heat ($c$) for each $π^{+}, π^{-}, π^{0}$ and the mixture pair data sets of pions generated by PYTHIA model at MB condition, indicate a transition from multifractality to monofractality in $pp$ collisions at $\sqrt{s}=13~$TeV.