The mean transverse momentum of ultracentral heavy-ion collisions: A new probe of hydrodynamics

We predict that the mean transverse momentum of charged hadrons $\langle p_t\rangle$ rises as a function of the charged-particle multiplicity in ultracentral nucleus-nucleus collisions. We explain that this phenomenon has a simple physical origin and represents an unambiguous prediction of the hydrodynamic framework of heavy-ion collisions. We argue that the relative increase of $\langle p_t \rangle$ is proportional to the speed of sound squared $c_s^2$ of the quark-gluon plasma. Based on the value of $c_s^2$ from lattice QCD, we expect $\langle p_t\rangle$ to increase by approximately $18$ MeV between 1\% and 0.001\% centrality in Pb+Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV.