Lévy-stable two-pion Bose-Einstein correlations in $\sqrt{s_{NN}}=200$ GeV Au$+$Au collisions

We present a detailed measurement of charged two- pion correlation functions in 0–30% centrality sNN=200 GeV Au+Au collisions by the PHENIX experiment at the Relativistic Heavy Ion Collider. The data are well described by Bose- Einstein correlation functions stemming from Levy-stable source distributions. Using a fine transverse momentum binning, we extract the correlation strength parameter λ, the Levy index of stability α, and the Levy length scale parameter R as a function of average transverse mass of the pair mT. We find that the positively and the negatively charged pion pairs yield consistent results, and their correlation functions are represented, within uncertainties, by the same Levy-stable source functions. The λ(mT) measurements indicate a decrease of the strength of the correlations at low mT. The Levy length scale parameter R(mT) decreases with increasing mT, following a hydrodynamically predicted type of scaling behavior. The values of the Levy index of stability α are found to be significantly lower than the Gaussian case of α=2, but also significantly larger than the conjectured value that may characterize the critical point of a second-order quark-hadron phase transition.