Assessing Mean Transverse Momentum of Ultracentral Collisions as a Tool for Extracting the Speed of Sound in Quark-Gluon Plasma

In high energy nuclear collisions, a new state of hot and dense matter, called quark-gluon plasma (QGP), is predicted to be formed. Experimentally constraining the equation of state (EoS) of QGP remains a key challenge. In steps towards quantifying the EoS, recent measurements by the Compact Muon Solenoid (CMS) experiment at the CERN’s Large Hadron Collider have spurred precise estimations of the speed of sound in QGP. These estimates assume that, in ultracentral collisions, the rate of change of the average transverse momentum (<p_T>) over the number of charged particles (N_ch), corresponds to the speed of sound. However, to what extent the speed of sound is quantitatively connected to this experimental observable has not been tested in a systematic way.

In this work, we apply a state-of-the-art relativistic hydrodynamic model, MUSIC, to conduct a comprehensive study of this assumption. By manipulating the input EoS which governs the speed of sound (e.g., varying from Lattice QCD calculations to hadronic gas and ideal gas models), we will present results on how the slope of <p_T> vs N_ch responds to EoS variations in the MUSIC model and compare with CMS data. Our findings will demonstrate the robustness and limitations of extracting the speed of sound via <p_T> in ultracentral collisions.