System-size dependence of the charged-particle pseudorapidity density at $\sqrt{s_{\rm NN}} = 5.02$ TeV for pp, p-Pb, and Pb-Pb collisions

We present the first systematic comparison of the charged-particle pseudorapidity densities for three widely different collision systems, pp, p-Pb, and Pb-Pb, at the top energy of the Large Hadron Collider ($\sqrt{s_{\rm NN}} = 5.02$ TeV) measured over a wide pseudorapidity range (${-3.5 <~\eta <~5}$), the widest possible among the four experiments at that facility. The systematic uncertainties are minimised since the measurements are recorded by the same experimental apparatus (ALICE). The distributions for p-Pb and Pb-Pb collisions are determined as a function of the centrality of the collisions, while results from pp collisions are reported for inelastic events with at least one charged particle at midrapidity. The charged-particle pseudorapidity densities are, under simple and robust assumptions, transformed to charged-particle rapidity densities. This allows for the calculation and the presentation of the evolution of the width of the rapidity distributions and of a lower bound on the Bjorken energy density, as a function of the number of participants in all three collision systems. We find a decreasing width of the particle production, and roughly a smooth ten fold increase in the energy density, as the system size grows, which is consistent with a gradually higher dense phase of matter.


Phys. Lett. B 845 (2023) 137730
HEP Data
e-Print: arXiv:2204.10210 | PDF | inSPIRE
Figure group

Figure 1

Charged-particle pseudorapidity density in Pb$-$Pb  and p$-$Pb for the $5\%$ most central collisions, and for pp collisions with INEL$>0$ trigger class. For symmetric collision systems (Pb$-$Pb and pp) the data has been symmetrised around ${\eta=0}$ and points for ${\eta>3.5}$ have been reflected around ${\eta=0}$. The boxes around the points and to the right reflect the uncorrelated and correlated, with respect to pseudorapidity, systematic uncertainty, respectively The relative correlated, normalisation, uncertainties are evaluated at ${\rm d}N_{\rm ch}/{\rm d}\eta|_{\eta=0}$. The lines show fits of Eq. 1 (Pb$-$Pb and pp) and Eq. 2 (p$-$Pb) to the data (discussed in Section 4). Please note that the ordinate has been cut twice to accommodate for the very different ranges of the charged-particle pseudorapidity densities.

Figure 2

Charged-particle pseudorapidity density in p$-$Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV in seven centrality classes based on the V0A and V0C estimators. The lines are obtained using a fit of a scaled, normal distribution in rapidity Eq. 2 to the data (discussed in Section 4).

Figure 3

Ratio ${r_X}$ of the charged-particle pseudorapidity density in Pb$-$Pb (top) and p$-$Pb (bottom) in different centrality classes to the charged-particle pseudorapidity density in pp in the INEL$>0$ event class. Note, for Pb$-$Pb $\eta_{\rm lab}$ is the same as the centre-of-mass pseudorapidity.

Figure 4

The width (top) and effective $p_{\rm T}/m$ (bottom) fit parameters as a function of the mean number of participants in pp, p$-$Pb, and Pb$-$Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV. Vertical uncertainties are the standard error on the best-fit parameter values, while horizontal uncertainties reflect the uncertainty on $\langle\N_{\rm part}\rangle$ from the Glauber calculations. Also shown are similar fit parameters from the same parameterisation of EPOS-LHC calculations as well as direct calculations of the standard deviation of the ${\rm d}N_{\rm ch}/{\rm d}y$ distributions and the $\langle p_{\rm T} \rangle / \langle m \rangle$ ratio from the EPOS-LHC calculations.

Figure 5

The transverse area $S_{\rm T}$ as calculated in a numerical Glauber model for two extreme cases: a) only the exclusive overlap of nucleons is considered (${\cap}$, open markers) and b) the inclusive area of participating nucleons contribute (${\cup}$, closed markers) in both p$-$Pb and Pb$-$Pb at $\sqrt{s_{\rm NN}}$ = 5.02 TeV.

Figure 6

Estimate of the lower bound on the Bjorken transverse energy density in pp, p$-$Pb, and Pb$-$Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV, considering the exclusive ($\cap$, open markers) and inclusive ($\cup$, full markers) overlap area $S_{\rm T}$ of the nucleons. The expression ${C N_{\rm part}^p}$ is fitted to case ${\cup}$, and we find $C=(0.8\pm0.3)$ ${\rm GeV}/({\rm fm^2}c)$ and ${p=0.44\pm0.08}$. Also shown is an estimate, via ${\rm d} E_{\rm T}/{\rm d}y$, of $\varepsilon_{\rm Bj}$ from Pb$-$Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV (stars with uncertainty band) .