Size of the quark-gluon plasma in ultracentral collisions: Impact of initial density fluctuations on the average transverse momentum

Recent experiments have shown that the mean transverse momentum $\langle p_T\rangle$ of outgoing particles increases as a function of the particle multiplicity in ultracentral nucleus-nucleus collisions at collider energies. This increase was originally predicted on the basis of simulations where the multiplicity increase occurred at constant volume, so that it implied a larger density and temperature. However, recent state-of-the-art simulations have shown that, for some models of initial condition, the volume may vary with the multiplicity in ultracentral collisions. We elucidate this effect by analytically relating the variation of the volume to the radial distribution of the one- and two-point functions of the fluctuating density field. We show that the volume variation is small if the total entropy of the ultracentral collisions scales with the mass number of the colliding isotopes. We argue that probing detailed transverse distributions of initial-state fluctuations through the ultracentral $\langle p_T\rangle$ has nontrivial implications for models of nuclear structure and of the pre-equilibrium stages.