Comparing effective temperatures in standard, Tsallis, and q-dual statistics from transverse momentum spectra of identified light charged hadrons produced in gold–gold collisions at RHIC energies

This study investigates the transverse momentum (\(p_T\)) spectra of identified light charged hadrons produced in gold–gold (Au+Au) collisions across various centrality classes at center-of-mass energies per nucleon pair, \(\sqrt{s_{NN}}\), ranging from 7.7 to 200 GeV, as measured by the STAR Collaboration at the Relativistic Heavy Ion Collider (RHIC). The analysis employs standard (Bose-Einstein/Fermi-Dirac), Tsallis, and q-dual statistics to fit the same \(p_T\) spectra and derive distinct effective temperatures: \(T_{\text {Standard}}\), \(T_{\text {Tsallis}}\), and \(T_{\text {q-dual}}\). In most instances, there exists an approximately linear relationship or positive correlation between \(T_{\text {Tsallis}}\) and \(T_{\text {Standard}}\), as well as between \(T_{\text {q-dual}}\) and \(T_{\text {Standard}}\), when considering \(T_{\text {Standard}}\) as a baseline. However, while both \(T_{\text {Tsallis}}\) and \(T_{\text {q-dual}}\) increase from semi-central to central Au+Au collisions at 62.4 GeV and 200 GeV, where QGP is expected, changes in \(T_{\text {Standard}}\) occur more gradually. This work suggests that \(T_{\text {Standard}}\) is better suited for characterizing phase transitions between hadronic matter and QGP compared to \(T_{\text {Tsallis}}\) or \(T_{\text {q-dual}}\), primarily due to the considerations related to entropy index in the Tsallis and q-dual statistics.