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Study of $\langle p_{\rm T} \rangle$ and its higher moments, and extraction of the speed of sound in Pb-Pb collisions with ALICE

The ALICE collaboration Abualrob, Ibrahim Jaser ; Acharya, Shreyasi ; Aglieri Rinella, Gianluca ; et al.
CERN-EP-2025-126, 2025.
Inspire Record 2933773 DOI 10.17182/hepdata.165515

Ultrarelativistic heavy-ion collisions create a quark-gluon plasma (QGP), a hot and dense state of strongly interacting QCD matter. In ultracentral collisions, the QGP volume remains nearly constant event-by-event, while its total entropy can fluctuate due to quantum effects, leading to temperature variations. These features allow the correlation between the mean transverse momentum $(\langle p_{\mathrm{T}} \rangle)$ of charged hadrons and their multiplicity to serve as a probe of the QGP's speed of sound, $c_{s}$. This study extracts $c_{s}$ by analyzing the relative increase in $\langle p_{\mathrm{T}} \rangle$ with respect to the charged-particle density $(\langle \mathrm{d}N_\mathrm{ch}/\mathrm{d}\eta \rangle)$ at midrapidity in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$, using data from the ALICE detector. Centrality is determined with estimators based on multiplicity and transverse energy, applying a pseudorapidity gap to reduce selection biases. The extracted value of $c_{s}^{2}$ is found to strongly depend on the employed centrality estimator and ranges between $0.1146 \pm 0.0028 \,\mathrm{(stat.)} \pm 0.0065 \,\mathrm{(syst.)}$ and $0.4374 \pm 0.0006 \mathrm{(stat.)} \pm 0.0184 \mathrm{(syst.)}$ in natural units. Additionally, the event-by-event $[p_{\mathrm{T}}]$ distribution is studied through its variance, skewness, and kurtosis. A pronounced decrease in the self-normalized variance and a peak followed by a drop in skewness suggest the suppression of impact-parameter fluctuations in ultracentral collisions. These observations provide new insights into the thermodynamic properties and initial-state fluctuations of the QGP.

35 data tables

Average number of participating nucleons ($\langle N_{\mathrm{part}} \rangle$) as a function of centrality percentile in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimators based on $N_{\mathrm{ch}}$, ${N_{\mathrm{tracklets}}}$, and $E_{\mathrm{T}}$ within $|\eta|\leq 0.8$.

Average number of participating nucleons ($\langle N_{\mathrm{part}} \rangle$) as a function of centrality percentile in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $N_{\mathrm{ch}} \in$ $-3.7<\eta<-1.7$ and $2.8 < \eta <5.1$.

Normalized $p_{\mathrm{T}}$-spectrum ratio as a function as a function of centrality in $\mathrm{Pb}-\mathrm{Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02~\mathrm{TeV}$. Data points are shown for centrality estimator based on $N_{\mathrm{ch}} \in$ $0.5 \leq |\eta|\leq 0.8$.

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Femtoscopic study of the proton-proton and proton-deuteron systems in heavy-ion collisions at the LHC

The ALICE collaboration Acharya, Shreyasi ; Aglieri Rinella, Gianluca ; Aglietta, Luca ; et al.
CERN-EP-2025-096, 2025.
Inspire Record 2917986 DOI 10.17182/hepdata.165812

This work reports femtoscopic correlations of p$-$p ($\bar{\rm p}-\bar{\rm p}$) and p$-$d ($\bar{\rm p}-\bar{\rm d}$) pairs measured in Pb$-$Pb collisions at center-of-mass energy $\sqrt{s_{\rm NN}}$ = 5.02 TeV by the ALICE Collaboration. A fit to the measured proton-proton correlation functions allows one to extract the dependence of the nucleon femtoscopic radius of the particle-emitting source on the pair transverse mass ($m_\text{T}$) and on the average charge particle multiplicity $\langle\text{dN}_\text{ch}/\text{d}\eta\rangle^{1/3}$ for three centrality intervals (0$-$10$\%$, 10$-$30$\%$, 30$-$50$\%$). In both cases, the expected power-law and linear scalings are observed, respectively. The measured p$-$d correlations can be described by both two- and three-body calculations, indicating that the femtoscopy observable is not sensitive to the short-distance features of the dynamics of the p$-$(p$-$n) system, due to the large inter-particle distances in Pb$-$Pb collisions at the LHC. Indeed, in this study, the minimum measured femtoscopic source sizes for protons and deuterons have a minimum value at $2.73^{+0.05}_{-0.05}$ and $3.10^{+1.04}_{-0.86}$ fm, respectively, for the 30$-$50$\%$ centrality collisions. Moreover, the $m_{\rm{T}}$-scaling obtained for the p$-$p and p$-$d systems is compatible within 1$\sigma$ of the uncertainties. These findings provide new input for fundamental studies on the production of light (anti)nuclei under extreme conditions.

23 data tables

proton-proton (same charge) correlation function for centrality 0-10% from Pb-Pb collisions at 5020 GeV

proton-proton (same charge) correlation function for centrality 10-30% from Pb-Pb collisions at 5020 GeV

proton-proton (same charge) correlation function for centrality 30-50% from Pb-Pb collisions at 5020 GeV

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Revealing the microscopic mechanism of deuteron formation at the LHC

The ALICE collaboration Acharya, Shreyasi ; Agarwal, Apar ; Aglieri Rinella, Gianluca ; et al.
CERN-EP-2025-081, 2025.
Inspire Record 2907586 DOI 10.17182/hepdata.165804

The formation of light (anti)nuclei with mass number A of a few units (e.g., d, $^3$He, and $^4$He) in high-energy hadronic collisions presents a longstanding mystery in nuclear physics [1,2]. It is not clear how nuclei bound by a few MeV can emerge in environments characterized by temperatures above 100 MeV [3-5], about 100,000 times hotter than the center of the Sun. Despite extensive studies, this question remained unanswered. The ALICE Collaboration now addresses it with a novel approach using deuteron-pion momentum correlations in proton-proton (pp) collisions at the Large Hadron Collider (LHC). Our results provide model-independent evidence that about 80% of the observed (anti)deuterons are produced in nuclear fusion reactions [6] following the decay of short-lived resonances, such as the $\Delta (1232)$. These findings resolve a crucial gap in our understanding of nucleosynthesis in hadronic collisions. Beyond answering the fundamental question on how nuclei are formed in hadronic collisions, the results can be employed in the modeling of the production of light and heavy nuclei in cosmic rays [7] and dark matter decays [8,9].

7 data tables

Measured $\pi^{+}$–d$\oplus\pi^{-}$–$\overline{\mathrm{d}}$ (left panel) correlation function.

Measured $\pi^{-}$–d$\oplus\pi^{+}$–$\overline{\mathrm{d}}$ (right panel) correlation function.

The extracted kinetic decoupling temperature is derived from $\pi^{+}$–d correlation functions.

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D$^{0}$-meson-tagged jet axes difference in proton-proton collisions at $\mathbf{\sqrt{\textit{s}} = 5.02}$ TeV

The ALICE collaboration Acharya, Shreyasi ; Agarwal, Apar ; Aglieri Rinella, Gianluca ; et al.
CERN-EP-2025-083, 2025.
Inspire Record 2907593 DOI 10.17182/hepdata.165764

Heavy-flavor quarks produced in proton-proton (pp) collisions provide a unique opportunity to investigate the evolution of quark-initiated parton showers from initial hard scatterings to final-state hadrons. By examining jets that contain heavy-flavor hadrons, this study explores the effects of both perturbative and non-perturbative QCD on jet formation and structure. The angular differences between various jet axes, $\Delta R_{\rm axis}$, offer insight into the radiation patterns and fragmentation of charm quarks. The first measurement of D$^{0}$-tagged jet axes differences in pp collisions at $\sqrt{s}=5.02$ TeV by the ALICE experiment at the LHC is presented for jets with transverse momentum $p_{\rm T}^{\rm ch~jet} \geq 10$${\rm GeV}/c$ and D$^0$ mesons with $p_{\rm T}^{\rm D^{0}} \geq 5$${\rm GeV}/c$. In this D$^0$-meson-tagged jet measurement, three jet axis definitions, each with different sensitivities to soft, wide-angle radiation, are used: the Standard axis, Soft Drop groomed axis, and Winner-Takes-All axis. Measurements of the radial distributions of D$^0$ mesons with respect to the jet axes, $\Delta R_{\mathrm{axis-D^0}}$, are reported, along with the angle, $\Delta R_{\mathrm{axis}}$, between the three jet axes. The D$^{0}$ meson emerges as the leading particle in these jets, closely aligning with the Winner-Takes-All axis and diverging from the Standard jet axis. The results also examine how varying the sensitivity to soft radiation with grooming influences the orientation of the Soft Drop jet axis, and uncover that charm-jet structure is more likely to survive grooming when the Soft Drop axis is further from the D$^{0}$ direction, providing further evidence of the dead-cone effect recently measured by ALICE.

16 data tables

$\Delta R_{\rm axis}$ distribution for $\rm STD-D^0$ for $\rm D^0$-tagged jets of $R=0.4$, in the intervals $10<p_{\rm T}^{\rm ch \ jet}<20 \ {\rm GeV}/c$ and $5<p_{\rm T}^{\rm D^0}<20 \ {\rm GeV}/c$.

$\Delta R_{\rm axis}$ distribution for $\rm WTA-D^0$ for $\rm D^0$-tagged jets of $R=0.4$, in the intervals $10<p_{\rm T}^{\rm ch \ jet}<20 \ {\rm GeV}/c$ and $5<p_{\rm T}^{\rm D^0}<20 \ {\rm GeV}/c$.

$\Delta R_{\rm axis}$ distribution for $\rm STD-WTA$ for $\rm D^0$-tagged jets of $R=0.4$, in the intervals $10<p_{\rm T}^{\rm ch \ jet}<20 \ {\rm GeV}/c$ and $5<p_{\rm T}^{\rm D^0}<20 \ {\rm GeV}/c$.

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Observation of the Onset of Constituent Quark Number Scaling in Heavy-Ion Collisions at RHIC

The STAR collaboration Aboona, B.E. ; Adam, J. ; Adamczyk, L. ; et al.
Phys.Rev.Lett. 135 (2025) 072301, 2025.
Inspire Record 2907591 DOI 10.17182/hepdata.159489

Partonic collectivity is one of the necessary signatures for the formation of quark-gluon plasma in high-energy nuclear collisions. Number of constituent quarks (NCQ) scaling has been observed for hadron elliptic flow $v_2$ in top energy nuclear collisions at the Relativistic Heavy Ion Collider and the LHC, and this has been theoretically suggested as strong evidence for partonic collectivity. In this Letter, a systematic analysis of $v_2$ of $π^{\pm}$, $K^{\pm}$, $K^{0}_{S}$, $p$, and $Λ$ in Au+Au collisions at ${\sqrt{s_{_{\rm{NN}}}}}$ = 3.2, 3.5, 3.9, and 4.5 GeV, with the STAR experiment at the Relativistic Heavy Ion Collider, is presented. NCQ scaling is markedly violated at 3.2 GeV, consistent with a hadronic-interaction dominated equation of state. However, as the collision energy increases, a gradual evolution to NCQ scaling is observed. This beam-energy dependence of $v_2$ for all hadrons studied provides evidence for the onset of dominant partonic interactions by ${\sqrt{s_{_{\rm{NN}}}}}$ = 4.5 GeV.

72 data tables

$p_{T}$ dependence of $v_{2}$ for $\pi^{+}$ in Au+Au collisions at 3 GeV

$p_{T}$ dependence of $v_{2}$ for $\pi^{+}$ in Au+Au collisions at 3.2 GeV

$p_{T}$ dependence of $v_{2}$ for $\pi^{+}$ in Au+Au collisions at 3.5 GeV

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Multiplicity-dependent inclusive J/$\psi$ production at forward rapidity in pp collisions at $\mathbf{\sqrt{s} = 13}$ TeV

The ALICE collaboration Acharya, Shreyasi ; Agarwal, Apar ; Aglieri Rinella, Gianluca ; et al.
JHEP 07 (2025) 238, 2025.
Inspire Record 2906995 DOI 10.17182/hepdata.159409

This paper presents a study of the inclusive forward J/$\psi$ yield as a function of forward charged-particle multiplicity in pp collisions at $\sqrt{s} = 13$ TeV using data collected by the ALICE experiment at the CERN LHC. The results are presented in terms of relative J/$\psi$ yields and relative charged-particle multiplicities with respect to these quantities obtained in inelastic collisions having at least one charged particle in the pseudorapidity range $|\eta| < 1$. The J/$\psi$ mesons are reconstructed via their decay into $\mu^+ \mu^-$ pairs in the forward rapidity region ($2.5 < y < 4$). The relative multiplicity is estimated in the forward pseudorapidity range $-3.7 < \eta < -1.7$, which overlaps with the J/$\psi$ rapidity region. The results show a steeper-than-linear increase of the J/$\psi$ yields versus the multiplicity. They are compared with previous measurements and theoretical model calculations.

1 data table

Forward inclusive J/$\psi$ relative yield as a function of the relative multiplicity in −3.7 < $\eta$ < −1.7 in INEL > 0 pp collisions at $\sqrt{s}$ = 13 TeV.


Precision Measurement of (Net-)proton Number Fluctuations in Au+Au Collisions at RHIC

The STAR collaboration Aboona, B.E. ; Adam, J. ; Adamczyk, L. ; et al.
Phys.Rev.Lett. 135 (2025) 142301, 2025.
Inspire Record 2906592 DOI 10.17182/hepdata.159490

We report precision measurements on cumulants ($C_{n}$) and factorial cumulants ($\kappa_{n}$) of (net-)proton number distributions up to fourth-order in Au+Au collisions from phase II of the Beam Energy Scan program at RHIC. (Anti-)protons are selected at midrapidity ($|y|<0.5$) within a transverse momentum range of $0.4 < p_T < 2.0$ GeV/$c$. The collision energy and centrality dependence of these cumulants are studied over center-of-mass energies $\sqrt{s_{NN}}$ = 7.7 -- 27 GeV. Relative to various non-critical-point model calculations and peripheral collision 70-80% data, the net-proton $C_4/C_2$ measurement in 0-5% collisions shows a minimum around 19.6 GeV for significance of deviation at $\sim2$--$5\sigma$. In addition, deviations from non-critical baselines around the same collision energy region are also seen in proton factorial cumulant ratios, especially in $\kappa_2/\kappa_1$ and $\kappa_3/\kappa_1$. Dynamical model calculations including a critical point are called for in order to understand these precision measurements.

14 data tables

Reference multiplicity distributions (RefMult3 and RefMult3X) for Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 GeV along with MC Glauber model fits.

Collision centrality dependence of net-proton cumulants in Au+Au collisions for $\sqrt{s_{NN}}$ = 7.7 - 27 GeV obtained with RefMult3 and RefMult3X centrality definition.

Collision energy dependence of net-proton cumulant ratios and proton factorial cumulant ratios in Au+Au collisions from $\sqrt{s_{NN}}$ = 7.7 - 200 GeV for 0-5$\%$ and 70-80$\%$ centrality. Data from $\sqrt{s_{NN}}$ = 7.7 - 27 GeV are from BES-II (obtained with RefMult3X except 27 GeV where RefMult3 is used). Data from $\sqrt{s_{NN}}$ = 39 - 200 GeV are from BES-I (RefMult3).

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First measurement of D$^{*+}$ vector spin alignment in Pb-Pb collisions at $\mathbf{\sqrt{s_{\rm NN}} = 5.02}$ TeV

The ALICE collaboration Acharya, Shreyasi ; Agarwal, Apar ; Aglieri Rinella, Gianluca ; et al.
CERN-EP-2025-072, 2025.
Inspire Record 2906994 DOI 10.17182/hepdata.165763

The first measurement of prompt D$^{*+}$-meson spin alignment in ultrarelativistic heavy-ion collisions with respect to the direction orthogonal to the reaction plane is presented. The spin alignment is quantified by measuring the element $\rho_{00}$ of the diagonal spin-density matrix for prompt D$^{*+}$ mesons with $4<p_{\rm T}<30$ GeV/$c$ in two rapidity intervals, $|y|<0.3$ and $0.3<|y|<0.8$, in central (0-10%) and midcentral (30-50%) Pb-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV. Evidence of spin alignment $\rho_{00}>1/3$ has been found for $p_{\rm T}>15$ GeV/$c$ and $0.3<|y|<0.8$ with a significance of $3.1\sigma$. The measured spin alignment of prompt D$^{*+}$ mesons is compared with the one of inclusive J/$\psi$ mesons measured at forward rapidity ($2.5 < y < 4$).

3 data tables

$\rho_{00}$ of prompt D$^{*\pm}$ mesons as a function of transverse momentum ($p_{\rm T}$) in the rapidity interval $0.0 < |y| < 0.3$ for mid-central (30--50\%) Pb--Pb collisions at $\sqrt{s_{\rm NN}}=5.02~TeV$.

$\rho_{00}$ of prompt D$^{*\pm}$ mesons as a function of transverse momentum ($p_{\rm T}$) in the rapidity interval $0.3 < |y| < 0.8$ for mid-central (30--50\%) Pb--Pb collisions at $\sqrt{s_{\rm NN}}=5.02~TeV$.

$\rho_{00}$ of prompt D$^{*\pm}$ mesons as a function of transverse momentum ($p_{\rm T}$) in the rapidity interval $0.0 < |y| < 0.3$ for central (0--10\%) Pb--Pb collisions at $\sqrt{s_{\rm NN}}=5.02~TeV$.


Measurement of correlations among net-charge, net-proton, and net-kaon multiplicity distributions in Pb-Pb collisions at $\sqrt{s_\text{NN}}=5.02$ TeV

The ALICE collaboration Acharya, Shreyasi ; Agarwal, Apar ; Aglieri Rinella, Gianluca ; et al.
JHEP 08 (2025) 210, 2025.
Inspire Record 2903549 DOI 10.17182/hepdata.160697

Correlations among conserved quantum numbers, such as the net-electric charge, the net-baryon, and the net-strangeness in heavy-ion collisions, are crucial for exploring the QCD phase diagram. In this letter, these correlations are investigated using net-proton number (as a proxy for the net-baryon), net-kaon number (for the net-strangeness), and net-charged particle number in Pb-Pb collisions at $\sqrt{s_\text{NN}}=5.02$ TeV with the ALICE detector. The observed correlations deviate from the Poissonian baseline, with a more pronounced deviation at LHC energies than at RHIC. Theoretical calculations of the Thermal-FIST hadron resonance gas model, HIJING, and EPOS LHC event generators are compared with experimental results, where a significant impact of resonance decays is observed. Thermal-FIST calculations under the grand canonical and canonical ensembles highlight significant differences, underscoring the role of local charge conservation in explaining the data. Recent lattice QCD studies have demonstrated that the magnetic field generated by spectator protons in heavy-ion collisions affects susceptibility ratios, in particular those related to the net-electric charge and the net-baryon numbers. The experimental findings are in qualitative agreement with the expectations of lattice QCD.

30 data tables

$\kappa^{2}_{\pi}$ as a function of centrality (%) in Pb$-$Pb collisions at $\sqrt{s_\mathrm{NN}}$ = 5.02 TeV for Set 1 $p_\mathrm{T}$ acceptance.

$\kappa^{2}_{\pi}$ as a function of centrality (%) in Pb$-$Pb collisions at $\sqrt{s_\mathrm{NN}}$ = 5.02 TeV for Set 2 $p_\mathrm{T}$ acceptance.

$\kappa^{2}_\mathrm{K}$ as a function of centrality (%) in Pb$-$Pb collisions at $\sqrt{s_\mathrm{NN}}$ = 5.02 TeV for Set 1 $p_\mathrm{T}$ acceptance.

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Investigating the p-$\pi^{\pm}$ and p-p-$\pi^{\pm}$ dynamics with femtoscopy in pp collisions at $\sqrt{s} = 13$ TeV

The ALICE collaboration Acharya, Shreyasi ; Agarwal, Apar ; Aglieri Rinella, Gianluca ; et al.
Eur.Phys.J.A 61 (2025) 194, 2025.
Inspire Record 2895576 DOI 10.17182/hepdata.159769

The interaction between pions and nucleons plays a crucial role in hadron physics. It represents a fundamental building block of the low-energy QCD dynamics and is subject to several resonance excitations. This work studies the p-$\pi^{\pm}$ dynamics using femtoscopic correlations in high-multiplicity pp collisions at $\sqrt{s} = 13$ TeV measured by ALICE at the LHC. As the final-state interaction between protons and pions is well constrained by scattering experiments and the study of pionic hydrogen, the results give access to information on the particle-emitting source in pp collisions using the femtoscopy methods. The scaling of the source size of primordial protons and pions against their pair transverse mass is extracted. The results are compared with the source sizes studied with p-p, p-K$^+$, and $\pi^{\pm}$-$\pi^{\pm}$ pairs by ALICE in the same collision system and are found to be in agreement for the different particle pairs. This reinforces recent findings by ALICE of a common emission source for all hadron-pairs in pp collisions at LHC energies. Furthermore, the p-p-$\pi^{\pm}$ systems are studied using three-particle femtoscopy in pp collisions at $\sqrt{s} = 13$ TeV. The presence of three-body effects is analyzed utilizing the cumulant expansion method. In this formalism, the known two-body interactions are subtracted in order to isolate the three-body effects. For both, p-p-$\pi^{+}$ and p-p-$\pi^{-}$, a non-zero cumulant is found, indicating effects beyond pairwise interactions. These results give information on the coupling of the pion to multiple nucleons.

52 data tables

p-$\pi^{+}$ + antip-$\pi^{-}$ correlation function in high-multiplicity (0-0.17%) pp collisions at $\sqrt{s}=13$ TeV for $m_\text{T} \in [0.54, 0.75)$ GeV/$c^2$

p-$\pi^{+}$ + antip-$\pi^{-}$ correlation function in high-multiplicity (0-0.17%) pp collisions at $\sqrt{s}=13$ TeV for $m_\text{T} \in [0.75, 0.95)$ GeV/$c^2$

p-$\pi^{+}$ + antip-$\pi^{-}$ correlation function in high-multiplicity (0-0.17%) pp collisions at $\sqrt{s}=13$ TeV for $m_\text{T} \in [0.95, 1.20)$ GeV/$c^2$

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