CMS-PAS-HIN-25-001

CMS-PAS-HIN-25-001
Probing thermodynamic properties of proton-lead collision systems via multiplicity dependence of average transverse momentum at the LHC
CMS Collaboration
1 May 2025

Abstract: The possible formation of hot, strongly interacting matter in small collision systems has generated significant interest. In this study, the correlation between the average transverse momentum ($ \langle {p_{\mathrm{T}}} \rangle $) and charged-particle multiplicity ($ N_{\mathrm{ch}} $) is analyzed in proton-lead (pPb) collisions at the CERN LHC to explore the system's thermodynamic properties. The analysis is performed over a broad multiplicity range using data collected by the CMS experiment, corresponding to an integrated luminosity of 186 nb$^{-1}$ at $ \sqrt{s_{\mathrm{NN}}}= $ 8.16 TeV and 0.509 nb$^{-1}$ at $ \sqrt{s_{\mathrm{NN}}}= $ 5.02 TeV. The squared speed of sound, $ c^2_{\mathrm{s}} $, is extracted from the correlation between $ \langle {p_{\mathrm{T}}} \rangle $ and $ N_{\mathrm{ch}} $ and studied as a function of an effective temperature estimated from the average transverse momentum. The extracted values are found to be comparable with lattice QCD predictions within uncertainties but are consistently higher than those predicted by the Trajectum hydrodynamic model. Comparisons with models that do not incorporate medium effects in pPb collisions show a poor agreement with data. These findings offer new insights into the possible thermodynamic properties of strongly interacting matter in small collision systems at LHC energies.
Links: CDS record (PDF) ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Mean $ p_{\mathrm{T}} $, $ \langle {p_{\mathrm{T}}} \rangle $, as a function of multiplicity, $ N_{\mathrm{ch}} $, for pPb collision energies of 5.02 TeV and 8.16 TeV, together with the fits used to extract the $ c^2_{\mathrm{s}} $ for data and HIJING simulations. Statistical uncertainties only are shown.
png pdf	Figure 2: Correlation $ d\ln{\langle {p_{\mathrm{T}}} \rangle}/d\ln{N_{\mathrm{ch}}} $ as a function of effective temperature $ ({=}\langle {p_{\mathrm{T}}} \rangle/X) $, where $ X $ is set to 3 for boost-invariant calculations and 2.45 for calculations accounting for asymmetries in the system. The results extracted from pPb collisions in this study are compared with lattice QCD predictions [60], previous measurements from ultra-central PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV by CMS [17], HIJING simulations, and the TRAJECTUM model for centrality estimator based on the energy sum in the hadron calorimeter for $ \|\eta\| < $ 0.8 (FCAL Cent.). Since the statistical uncertainties are negligible, the black error bars in the pPb data represent systematic uncertainties only. Theoretical uncertainties are taken from Ref. [40]. The HIJING results are presented with statistical uncertainties only.
png pdf	Figure 2-a: Correlation $ d\ln{\langle {p_{\mathrm{T}}} \rangle}/d\ln{N_{\mathrm{ch}}} $ as a function of effective temperature $ ({=}\langle {p_{\mathrm{T}}} \rangle/X) $, where $ X $ is set to 3 for boost-invariant calculations and 2.45 for calculations accounting for asymmetries in the system. The results extracted from pPb collisions in this study are compared with lattice QCD predictions [60], previous measurements from ultra-central PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV by CMS [17], HIJING simulations, and the TRAJECTUM model for centrality estimator based on the energy sum in the hadron calorimeter for $ \|\eta\| < $ 0.8 (FCAL Cent.). Since the statistical uncertainties are negligible, the black error bars in the pPb data represent systematic uncertainties only. Theoretical uncertainties are taken from Ref. [40]. The HIJING results are presented with statistical uncertainties only.
png pdf	Figure 2-b: Correlation $ d\ln{\langle {p_{\mathrm{T}}} \rangle}/d\ln{N_{\mathrm{ch}}} $ as a function of effective temperature $ ({=}\langle {p_{\mathrm{T}}} \rangle/X) $, where $ X $ is set to 3 for boost-invariant calculations and 2.45 for calculations accounting for asymmetries in the system. The results extracted from pPb collisions in this study are compared with lattice QCD predictions [60], previous measurements from ultra-central PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV by CMS [17], HIJING simulations, and the TRAJECTUM model for centrality estimator based on the energy sum in the hadron calorimeter for $ \|\eta\| < $ 0.8 (FCAL Cent.). Since the statistical uncertainties are negligible, the black error bars in the pPb data represent systematic uncertainties only. Theoretical uncertainties are taken from Ref. [40]. The HIJING results are presented with statistical uncertainties only.
png pdf	Figure 3: Mean transverse momentum as a function of charged-particle multiplicity, both normalized to reference values obtained for the $ E_{\mathrm{T, sum}}^{\mathrm{HF}} $ centrality range of 0-0.01%. Results are shown for pPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV and 8.16 TeV, along with HIJING simulations at 8.16 TeV presented with statistical uncertainties only.

Tables
png pdf	Table 1: Centrality and corresponding $ E_{\mathrm{T, sum}}^{\mathrm{HF}} $ intervals for the two pPb collision energies.

Summary

In this note, a study of the thermodynamic properties of pPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 8.16 TeV and 5.02 TeV is presented by analyzing the multiplicity dependence of the average transverse momentum, $ \langle {p_{\mathrm{T}}} \rangle $. The squared speed of sound, $ c^2_{\mathrm{s}} $, in a hot QCD medium has been extracted following the approach established in Ref. [13], where fixed intervals in the transverse energy sum in the forward calorimeters serve as a proxy for fixing the effective medium volume, while variations in collision energy allow for the determination of $ c^2_{\mathrm{s}} $. The extracted values of $ c^2_{\mathrm{s}} $ are found to be systematically lower than lattice QCD calculations but overall consistent within experimental and theoretical uncertainties, depending on the estimate of the effective temperature, which is model dependent. The results are also close (systematically above) to a full hydrodynamic boost-invariant TRAJECTUM model. Additionally, the dependence of $ \langle {p_{\mathrm{T}}} \rangle $ on charged-particle multiplicity, $ N_{\mathrm{ch}} $, has been analyzed up to the highest multiplicities available in the dataset. An indication of a similar increasing trend of $ \langle {p_{\mathrm{T}}} \rangle $ with $ N_{\mathrm{ch}} $, previously observed in ``ultra-central'' PbPb collisions, has been identified for very high multiplicity pPb events, although it is much less pronounced than in PbPb data. The HIJING model at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 8.16 TeV fails to describe the observed trend in the data, suggesting that key physical mechanisms governing bulk particle production in pPb collisions remain to be understood. These studies offer new insights into the thermodynamic properties of pPb collisions and have the potential to provide additional constraints on the equation of state of QCD matter in small collision systems.

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