The size of the quark-gluon plasma in ultracentral collisions: impact of initial density fluctuations on the average transverse momentum

Abstract

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.

Figures (7)

• Figure 1: Histogram of the distribution of the total entropy in a simulation of $10^7$ minimum-bias events for various values of $\nu$, rescaled by its average value at $b=0$, $S_{\rm knee}$. For each value of $\nu$, the fluctuation parameter $k$ has a different value determined according to Eq. (\ref{['varS']}). We also plot the distribution of the charged multiplicity measured by ATLAS ATLAS:2024jvf, rescaled in the same way. The shaded area displays the distribution of the total entropy for events with $b=0$ for $\nu=0.5$, rescaled by a factor 1/100. It is essentially identical for other values of $\nu$, as a consequence of the constraint (\ref{['varS']}).
• Figure 2: Entropy density profiles of collisions with $b=0$, rescaled by a global factor $S_{\rm knee}$ for each $\nu$. We vary $\nu$ in Eq. (\ref{['defnu']}), keeping the position of nucleons fixed. The gamma fluctuations normalizing each participant nucleon are however sampled independently for each plot (different $k$ parameters).
• Figure 3: Variation of the average value of $R^2$ (Eq. (\ref{['defR']})) with the total entropy $S$ (Eq. (\ref{['defS']})) in Pb+Pb collisions in the T$\mathrel{\raisebox{-2.1pt}{R}}$ENTo model, for various values of the exponent $\nu$ in Eq. (\ref{['defnu']}). As in Fig. \ref{['fig:histos']}, we rescale $S$ by $S_{\rm knee}$. Dotted line: minimum-bias events. Solid lines: events with $b=0$. Dashed lines: perturbative expression for $b=0$, Eq. (\ref{['R2versusS']}).
• Figure 4: Variation of the mean entropy density $\kappa_1(r)$ (circles, Eq. (\ref{['defkappa1']})) and of the correlation $\kappa_2(r)$ (squares) between entropy density and total entropy (Eq. (\ref{['defkappa2']})) for three different values of the exponent $\nu$ in Eq. (\ref{['defnu']}). These functions are scaled by $S_{\rm knee}$ and $\sigma^2_S$, respectively, in such a way that they integrate to unity over the transverse plane.
• Figure 5: Variation of $R_1^2$ and $R_2^2$, defined by Eqs. (\ref{['defR1']}) and (\ref{['defR2']}), with the exponent $\nu$ in Eq. (\ref{['defnu']}).