Universality of scaled particle spectra in ultrarelativistic heavy-ion collisions

TL;DR

The paper investigates whether the full transverse momentum spectra in ultrarelativistic nuclear collisions possess a universal spectral shape once global scales are removed. It defines the scaled spectrum $U(x_T)$ with $x_T = p_T / \langle p_T\rangle$ and studies its universality both in event-by-event hybrid hydrodynamic simulations and in ALICE data across Pb-Pb, Xe-Xe, p-Pb, and p-p systems. The results show near-perfect event-by-event universality and centrality-independent curves for large and mid-size systems, with universal behavior breaking down at large $p_T$ and in the smallest systems, pointing to a hydrodynamic origin in many cases. This scaling behavior offers a potential signature of fluid-like QCD matter and provides a framework to probe collectivity in small systems, guiding future experiments and theory across different energies and collision systems.

Abstract

We study the transverse momentum spectra of identified particles in ultrarelativistic collisions of large and small collision systems. In order to isolate information contained in the momentum dependence, we propose to scale the spectra by the total particle number and mean transverse momentum -- global quantities which are already well studied. We observe an interesting, nearly universal, centrality-independent shape in the scaled spectra, similar to scalings that have been studied previously. This scaling behavior breaks down at large transverse momentum and for very small systems, such as those produced in p-p collisions. We perform hybrid hydrodynamic simulations and show that, in these simulations, a centrality-independent shape is a consequence of an event-by-event independence. Our results motivate further theoretical and experimental investigations of the regime of validity of this scaling phenomenon and their physical interpretation at different collision energies and systems.

Figures (3)

• Figure 1: (left) Presents the pion, $\pi^++\pi^-$, $p_T$-spectra for Pb-Pb at 2.76 TeV minimum bias, in the hybrid simulations. (right) Scaled spectra for each event, $U_{\rm ev}(x_T)=(\left\langle p_T \right\rangle_{\rm ev}/N_{\rm ev})dN_{\rm ev}/dp_T$, computed using Eq. \ref{['eq:universal']}, for the events in the left plot. Centrality-independent universal behavior in $U_{\rm ev}(x_T)$ is observed.
• Figure 2: (a) The scaled spectra, Eq. \ref{['eq:universal']}, for $\pi^++\pi^-$ in Pb-Pb at 2.76 TeV and 5.02 TeV, and p-Pb 5.02 TeV, computed using hybrid simulations. Once the system is fixed, there is universality across centralities. (b) The ratio between $U$ coming from four centralities and $U$ for the most central collisions in Pb-Pb 2.76 TeV. (c) Ratio between $U$ coming from four centralities and $U$ for the most central collisions in Pb-Pb 5.02 TeV. (d) Ratio between $U$ coming from four centralities and $U$ for the most central collisions in p-Pb 5.02 TeV. We note that 99$\%$ of the pions are produced to the left of the vertical gray lines. The ExTrEME simulations (b) used the parameters from NunesdaSilva:2020bfs, and the hybrid simulation presented in (c) and (d) used Duke parameters Moreland:2018gshdaSilva:2022xwu.
• Figure 3: (a) The scaled spectra $U(x_T)$, as defined in Eq. \ref{['eq:universal']}, for $\pi^+ + \pi^-$ in Pb-Pb at 2.76 TeV pb276ALICE:2013mez and 5.02 TeV pb502ALICE:2019hno, Xe-Xe 5.44 TeV ALICE:2021lsv, p-Pb 5.02 TeV ppb502ALICE:2013wgn, and p-p 7 TeV pp7ALICE:2018pal from experimental data. The ratio between $U$ coming from four centralities and $U$ for the most central collisions is shown in (b) for Pb-Pb 2.76 TeV, (c) for Pb-Pb 5.02 TeV, (d) for Xe-Xe 5.44 TeV, (e) for p-Pb 5.02 TeV and (f) for p-p 7 TeV. 99$\%$ of the pions are produced to the left of the vertical gray lines. The p-p data is sorted by event activity, similar to centrality in heavy-ions, but with non-uniform percentile bin widths. We follow ALICE and simply label them with Roman numerals I--IX. See Table I of pp7ALICE:2018pal for the corresponding percentiles.