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 \(\sqrt{s_{_{NN}}}=200\) 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 Lévy-stable source distributions. Using a fine transverse momentum binning, we extract the correlation strength parameter \(\lambda\), the Lévy index of stability \(\alpha\) and the Lévy length scale parameter \(R\) as a function of average transverse mass of the pair \(m_T\). 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 Lévy-stable source functions. The \(\lambda(m_T)\) measurements indicate a decrease of the strength of the correlations at low \(m_T\). The Lévy length scale parameter \(R(m_T)\) decreases with increasing \(m_T\), following a hydrodynamically predicted type of scaling behavior. The values of the Lévy index of stability \(\alpha\) are found to be significantly lower than the Gaussian case of \(\alpha=2\), but also significantly larger than the conjectured value that may characterize the critical point of a second-order quark-hadron phase transition.