γ-charge correlation in heavy ion collisions: Various approaches

Abstract

Event-by-event $\ensuremath{\gamma}$-charge ($\ensuremath{\gamma}\text{-ch}$) correlation is studied for systems going through QCD chiral phase transition. In this paper, various methods for measuring $\ensuremath{\gamma}\text{-ch}$ correlation in heavy ion collisions are discussed. Dynamical fluctuation due to the formation of domains of disoriented chiral condensate (DCC) that can affect $\ensuremath{\gamma}\text{-ch}$ correlation is addressed. We have studied known detector and statistical effects involved in these measurements and suggest suitable robust observables $\ensuremath{\Delta}{\ensuremath{\nu}}_{\mathrm{dyn}}$ and ${r}_{m,1}$ sensitive to small $\ensuremath{\gamma}\text{-ch}$ correlation signals. These observables are constructed based on moments of multiplicity distributions of photons and charged particles. Estimations of measurable signals from various available models such as an ideal Boltzmann gas of pions, Monte Carlo models based on transport, and minijets are discussed. Collision centrality dependence of the observables is estimated from the central limit theorem and is found to be consistent with the model predictions. Observables are found to be highly sensitive to the fraction of DCC events and to have nonlinear dependence on the fraction of pions carrying DCC signals. The variation of ${r}_{m,1}$ with order $m$ of its moments is sensitive to the nature and strength of the $\ensuremath{\gamma}\text{-ch}$ correlation.