Macroscopic properties

Objective of the ALICE is to investigate the QGP created at center-of-mass energies ranging from a few TeV. A crucial aspect of this research is estimating the initial energy density and temperature necessary for QGP formation in collisions. The initial energy density can be inferred from the observed hadron production in the final state of the fireball across different collision centrality classes and at varying center-of-mass energies. Figure 2 from [15] illustrates the scaled charged-particle multiplicity measured at midrapidity (|y| < 0.5), normalized by $\langle N_{\text{part}}\rangle /2$, in various collision systems, including pp, $\text{p}\overline{\text{p}}$, p(d)A, and central heavy-ion collisions, plotted against the center-of-mass energy per nucleon pair, $\sqrt{s}$. ALICE has contributed data from Pb-Pb collisions at $\sqrt{s_{\text{NN}}}=2.76\text{ TeV}$ and 5.02 TeV, Xe-Xe collisions at $\sqrt{s_{\text{NN}}}=5.44\text{ TeV}$, and pp($\overline{\text{p}}$, Pb) collisions spanning a broad range of $\sqrt{s}$ from the TeV range to above 10 TeV. The dependence of $\frac{2}{\langle N_{\text{part}}\rangle }\langle \frac{\text{d}{N}_{\text{ch}}}{\text{d}\eta }\rangle$ on $\sqrt{s_{\text{NN}}}$ was fitted with a function of α × sβ. The fitting results yielded β = 0.152 ± 0.003 for central A-A collisions and β = 0.103 ± 0.002 for p-p and p(d)-A collisions. This indicates that heavy-ion collisions are significantly more efficient in converting initial beam energy into particle production at midrapidity compared to pp or p-Pb collisions [15].

Fig. 2Full-screen View

(Color online) Collision energy dependence of charged-particle pseudorapidity density at midrapidity (|y|<0.5) normalized to average number of participants, $\frac{2}{\langle N_{\text{part}}\rangle }\langle \text{d}{N}_{\text{ch}}/\text{d}\eta \rangle$

The size dependence of particle production in collision systems ranging from p-p(Pb) to Xe-Xe and Pb-Pb has been measured with unprecedented precision. Figure 3 from [15] illustrates the centrality dependence of $\langle N_{\text{part}}\rangle$ on $\frac{2}{\langle N_{\text{part}}\rangle }\langle \frac{\text{d}{N}_{\text{ch}}}{\text{d}\eta }\rangle$. Data were collected from Pb-Pb and Xe-Xe collisions at $\sqrt{s_{\text{NN}}}=5.02\text{ TeV}$ and 5.44 TeV, respectively, as well as from Au-Au and Cu-Cu collisions at RHIC energy setups. Uncertainties range from approximately 3% for central A-A collisions at midrapidity to approximately 10% for peripheral results in the forward region. Results at $\sqrt{s_{\text{NN}}}=5.02$ TeV were scaled using factors calculated from the fit function in Fig. 2 for the top 5% most central Au-Au, Cu-Cu, and Xe-Xe collisions. At the same $\langle N_{\text{part}}\rangle$, the shape of $\frac{2}{\langle N_{\text{part}}\rangle }\langle \frac{\text{d}{N}_{\text{ch}}}{\text{d}\eta }\rangle$ as a function of $\langle N_{\text{part}}\rangle$ exhibited slightly more variability in Xe-Xe compared to Pb-Pb, with a similar pattern observed between Au-Au and Cu-Cu collision systems. Reference [15] noted that these deviations, while present, are not significant given the large uncertainties, and could be attributed to the different Glauber model simulations used to estimate $\langle N_{\text{part}}\rangle$ in ALICE [16] and RHIC [17]. Comparison to PYTHIA 8.3 [18] calculations in Fig. 3, with different centrality selection methods (e.g., N_ch-selected and N_part-selected), revealed variations in the dependence of $\frac{2}{\langle N_{\text{part}}\rangle }\langle \frac{\text{d}{N}_{\text{ch}}}{\text{d}\eta }\rangle$, suggesting fluctuations in charged-particle multiplicity at a fixed number of particle sources.

Fig. 3Full-screen View

(Color online) Values of $\frac{2}{\langle N_{\text{part}}\rangle }\langle \frac{\text{d}{N}_{\text{ch}}}{\text{d}\eta }\rangle$ are compared in various collisions

Particle production measurements are pivotal in estimating the initial energy density and temperature, which are crucial for determining whether the conditions for the QCD phase transition are met during collisions [19-26]. The energy density in the collision can be estimated using the “Bjorken estimate” [27]: ϵ(τ), which is derived from the total produced transverse momentum. This estimation method applies to a system that undergoes free-streaming with boost-invariant longitudinal expansion and no transverse expansion, as described in references [27, 15]. By using the measured charged-particle pseudorapidity density and assuming a normal distribution of charged particles in rapidity [28, 29], it becomes feasible to derive a lower-bound estimate of the energy density ${\epsilon }_{\text{LB}}$ multiplied by the formation time τ in the collisions [30]. The transverse area S_T is determined using the Glauber model [31], which accounts for all participating nucleons. Figure 4 illustrates the resulting product ${\epsilon }_{\text{LB}}\tau$ for pp, p-Pb, and Pb-Pb collisions at $\sqrt{s_{\text{NN}}}$ = 5.02 TeV, as well as Pb-Pb collisions at $\sqrt{s_{\text{NN}}}$ = 2.76 TeV. A power-law fit $a{N}_{\text{part}}^{\text{p}}$ applied to the data indicates a significant increase in the energy density with the increasing transverse area of the initial overlap between the colliding nuclei [15].

Fig. 4Full-screen View

(Color online) Lower-bound estimate of the energy density times the formation time τ in pp, p-Pb, and Pb–Pb collisions at $\sqrt{s_{\text{NN}}}$ = 5.02 TeV as a function of the number of participants [30]

Another critical parameter in determining the formation of QGP is the temperature of the system created in collisions. It is important to distinguish between two concepts of temperature: the chemical freeze-out temperature [32] and the kinetic freeze-out temperature [33]. These temperatures characterize the thermodynamic properties of the fireball at the stages of chemical equilibrium and ceasing of hadron rescattering, respectively. The measurement of the kinetic freeze-out temperature has incorporated light nuclei to explore the system’s thermalization [34]. Owing to their large mass, (anti-)α production yields and transverse-momentum spectra are particularly significant as they rigorously test particle production models. The combined anti-α and α spectrum, when included in a common blast-wave fit with lighter particles, indicates that the (anti-)α also participates in the collective expansion of the collision medium. A blast-wave fit using only protons, (anti-)α, and other light nuclei yields a flow velocity comparable to that from a fit including all particles. However, fitting only protons and light nuclei results in a similar flow velocity but a notably higher kinetic freeze-out temperature, as shown in Fig. 5. Interestingly, hypernuclei exhibit a similar flow velocity and kinetic freeze-out temperature to light nuclei [35, 36], although more data from ALICE Run 3 is needed to solidify these findings [35].

Fig. 5Full-screen View

(Color online) Combined blast-wave fit of all available light flavored hadron p_T spectra including nuclei [37, 38] (left) and only p, $\overline{\text{d}}$, $\overline{\text{t}}$, ${}^3\overline{\text{He}}$ and ⁴He p_T spectra (right) in Pb–Pb collisions at $\sqrt{s_{\text{NN}}}=5.02\text{ TeV}$ for 0%–10% central events (upper panels). Lower panels show ratio between each data point and blast-wave model fit for each species

The temperature of the early partonic phase can be experimentally accessed through sensitive probes produced in the early stages of collisions, such as heavy-flavor $\text{q}\overline{\text{q}}$ states (quarkonia) and electromagnetic radiation. Since the seminal work by Matsui and Satz [39], quarkonium has been proposed as a thermometer for the QGP. The strong binding potential between quark and antiquark pairs is screened by color charges in the dense and hot medium, leading to the “melting” of $\text{q}\overline{\text{q}}$ states. This phenomenon offers the opportunity to correlate the production or suppression of quarkonia with the temperature of the QGP. A detailed discussion on quarkonia and dileptons will be presented in Sect. 2.3.

The temperature can be experimentally accessed through the measurement of thermal photons emitted by the hot plasma, as their production rate provides insights into the early conditions of the QGP. Direct photons are those that do not originate from parton fragmentation or hadronic decays but are instead produced by electromagnetic interactions during various stages of the collision. Figure 6 presents the direct photon spectra measured in Pb–Pb collisions at 2.76 TeV by the ALICE collaboration [40] and in Au-Au collisions at 0.2 TeV by the PHENIX collaboration [42, 41] in the 0-20% and 20-40% centrality classes. Thermal photons dominate the low transverse-momentum region ($p_{\text{T}}\lesssim 3$ GeV/c), following an approximately exponential behavior characterized by ${\text{d}}^2{N}_{{\gamma }_{\text{dir}}}/\left(p_{\text{T}}\text{d}{p}_{\text{T}}\text{d}y\right)\propto e^{-p_{\text{T}}/T_{\text{eff}}}$. The inverse logarithmic slope T_eff accounts for the radial expansion of the system, causing a blue-shift of emitted photons [45]. At higher momenta ($p_{\text{T}}\gtrsim 5$ GeV/c), the direct photon spectrum includes contributions from “prompt” photons, which originate from initial hard scatterings and the subsequent interaction of hard scattered partons with the medium (referred to as “jet-photon conversion”). The invariant yield of direct photons is determined by first measuring the excess of direct photons over decay photons, denoted by Rγ. Figure 6 presents Rγ for central and semi-central Pb–Pb collisions at = 2.76 TeV. At high momenta ($p_{\text{T}}\gtrsim 5$ GeV/c), the ratio Rγ indicates consistency with prompt photon production predicted by perturbative Quantum Chromodynamics (pQCD) and JETPHOX calculations [46, 47]. The excess of direct photons observed at low transverse momentum (0.9 GeV/c < p_T < 2.1 GeV/c) suggests an abundance of thermal photons originating from the Quark-Gluon Plasma (QGP). This region, dominated by thermal direct photons, is fitted with an exponential function to extract the effective temperature (T_eff), yielding values of T_eff = (304 ± 41) MeV and T_eff = (407 ± 114) MeV for central and semi-central Pb–Pb collisions, respectively. Comparing these temperatures to the slopes of the spectra measured by PHENIX, an increase in the effective temperature from RHIC to the LHC is evident. However, directly determining the initial temperature of the fireball remains challenging and has not yet been achieved, as it requires model calculations that account for the evolution of the QGP medium and radial flow effects, as discussed in [15].

Fig. 6Full-screen View

(Color online) Direct photon spectra (top) and direct photon excess Rγ (bottom) measured in Pb–Pb collisions at 2.76 TeV [40] and in Au-Au collisions at 0.2 TeV [41, 42] in 0%–20% (left) and 20–40% (right) centrality classes

The system size and lifetime are crucial indicators of the fireball properties created in collisions, assessed through particle momentum correlations, known as femtoscopy, at the final kinetic freeze-out state. Historically referred to as “HBT interferometry” after its originators Hanbury-Brown and Twiss in the 1950s and 1960s in astronomy [48, 49], femtoscopy involves constructing relative momentum correlations and fitting them to extract particle interaction and source parameters (see Sect. 2.2). The volume measured by femtoscopy corresponds to the size of the emitting source, known as the homogeneity volume, which typically differs from the total volume of the system at freeze-out [50].

The upper portion of Fig. 7 illustrates how the size of the homogeneity region, inferred from femtoscopic pion radii, scales with the charged-particle pseudorapidity density. These measurements were conducted in central p-Pb and Au-Au collisions across various energy regimes. Notably, the size of the homogeneity region increases approximately threefold from AGS energies to the LHC [15]. The decoupling time of the system is commonly approximated using the decoupling time of pions, ${\tau }_{\text{f}}$, owing to their predominant abundance (approximately 80%) within the system. The lower panel of Fig. 7 illustrates ${\tau }_{\text{f}}$ alongside global data. It shows a linear increase with the cube root of the charged-particle pseudorapidity density, starting from 4-5 fm/c at AGS energies, rising to 7-8 fm/c at the highest RHIC energies, and reaching 10-11 fm/c in central Pb–Pb collisions at $\sqrt{s_{\text{NN}}}$ = 2.76 TeV.

Fig. 7Full-screen View

(Color online) Homogeneity volume (top) and decoupling time τ_f (bottom) measured at 2.76 TeV [43, 44] compared to those obtained at experiments at lower energies. Homogeneity region is determined as product of three pion femtoscopic radii at $\langle k_{\text{T}}\rangle =0.3$ GeV/c for 0–5% central events

Flow and correlations

The dynamic behavior of the QGP provides crucial insights into strongly interacting matter. These properties are primarily defined by measurements of the collective motion of final-state particles generated in heavy-ion collisions. Anisotropic flow, quantified by Fourier coefficients of the particle azimuthal distributions with respect to symmetry plane angles, Ψ, is a key observable. A cornerstone in exploring the strongly coupled QGP paradigm involves extensive measurements of elliptic flow (v₂) and triangular flow (v₃), the second- and third-order components of anisotropic flow, respectively. Characteristic features of v₂ measurements include mass ordering, particle species grouping (e.g., mesons and baryons), and number of constituent quarks (NCQ) scaling. These features can be interpreted as the interplay between the dominant ellipsoidal geometry in the initial state, the collective expansion of the system, and hadronization through quark coalescence. Overall, these measurements suggest the creation of an “ideal fluid” in relativistic heavy-ion collisions.

Beyond measuring v₂, studying v₂ fluctuations can provide deeper insights into the collective behavior of the QGP. In [52], the elliptic flow of identified hadrons in Pb–Pb collisions at $\sqrt{s_{\text{NN}}}$ = 5.02 TeV is measured using two- (v₂｛2｝) and four- (v₂｛4｝) particle cumulants. By combining data for both v₂｛2｝ and v₂｛4｝, ALICE presents the first measurements of mean elliptic flow, elliptic flow fluctuations, and relative elliptic flow fluctuations for various hadron species, probing event-by-event eccentricity fluctuations in the initial state as well as contributions from the dynamic evolution of the expanding QGP. When compared with hydrodynamic calculations incorporating quark coalescence, differences in the relative flow fluctuations for different particle species are observed, suggesting that final-state hadronic interactions further modify these fluctuations.

The correlations between event-by-event fluctuations of two different flow amplitudes are commonly quantified using “symmetric cumulant” (SC) observables. Building on previous measurements [53], ALICE has extended event-by-event correlations to include three flow amplitudes in higher-order SC observables [54]. These three-harmonic correlations emerge during the collective evolution of the medium and differ from those present in the initial state, which cannot be explained by previous lower-order flow measurements. They provide the first constraints on the nonlinear response contribution in v₅ from v₂ and v₃, enhancing our understanding of the event-by-event flow fluctuation patterns in the QGP.

In recent years, striking similarities between numerous observables, including the “ridge” structure, have been observed in A-A and high-multiplicity p-A and pp collisions at both RHIC and LHC energies, revealing the presence of collectivity in small-system collisions. To investigate the “smallest” (p-A, pp, ee...) and “dilutest” (lower multiplicity) limit of collectivity onset, various measurements are performed in ALICE. In [51], flow coefficients and their cross-correlations using two- and multiparticle cumulants are studied and compared in collisions of pp at $\sqrt{s}$ = 13 TeV, p-Pb at $\sqrt{s_{\text{NN}}}$ = 5.02 TeV, Xe–Xe at $\sqrt{s_{\text{NN}}}$ = 5.44 TeV, and Pb-Pb at $\sqrt{s_{\text{NN}}}$ = 5.02 TeV, as shown in Fig. 8. The multiplicity dependence of vn is measured over a wide range. An ordering of the coefficients v₂ > v₃ > v₄ is observed in pp and p-Pb collisions, similar to that seen in large collision systems. However, a weaker v₂ multiplicity dependence is found compared to A-A collisions within the same range. In Fig. 9, the v₂ measurements for charged π, K, and p are presented and compared with state-of-the-art Hydro-Coal-Frag calculations incorporating quark coalescence [55]. A characteristic grouping and splitting of v₂ for baryons and mesons is observed. The NCQ scaling is further examined and found to approximately hold [56], as shown in Fig. 10. These results collectively confirm the existence of partonic collectivity.

Fig. 8Full-screen View

(Color online) Multiplicity dependence of vn for pp, p-Pb, Xe–Xe and Pb–Pb collisions. [51]

Fig. 9Full-screen View

(Color online) p_T-differential v₂ measured with two-particle correlation for various hadrons in p–Pb collisions at $\sqrt{s_{\text{NN}}}$ = 5.02 TeV is compared with calculations from the Hydro-Coal-Frag model. [55]

Fig. 10Full-screen View

(Color online) The NCQ scaling for various baryons and mesons measured in p-Pb collisions at $\sqrt{s_{\text{NN}}}$ = 5.02 TeV, indicating the existence of partonic collectivity. [56]

In Ref. [51], a novel subevent method is employed, revealing that v₂ measured with four-particle cumulants aligns well with that from six-particle cumulants in pp and p-Pb collisions. The correlation magnitude between $v_n^2$ and $v_m^2$, assessed with the aforementioned SC, is consistently positive across all multiplicities for v₂ and v₄. Conversely, for v₂ and v₃, the correlation is negative and changes sign at low multiplicity, indicating a different fluctuation pattern for vn.

The measurement of near-side associated per-trigger yields (ridge yields) from the analysis of angular correlations of charged hadrons is performed in pp collisions at $\sqrt{s}$ = 13 TeV [57]. A prominent jet-fragmentation peak, resulting from the correlations of particles originating from the fragmentation of the same parton, is clearly observed. A broad away-side structure emerges from the correlations of tracks from back-to-back jet fragments, spreading across the entire $\text{Δ}\eta$ region. As illustrated in Fig. 11, an enhancement of the correlation, known as the “ridge” structure, is visible at $\left|\text{Δ}\eta \right|>1.4$ and $\text{Δ}\varphi =0$. This ridge, observed in previous measurements, is interpreted in heavy-ion collisions as indicative of the collective expansion of the QGP medium. Long-range ridge yields are extracted, extending into the low-multiplicity region where a strongly interacting medium is typically unlikely to form. The precision of these new low-multiplicity results enables the first direct quantitative comparison with results obtained in e⁺e^- collisions, as shown in Fig. 12. In e⁺e^- collisions, initial-state effects such as preequilibrium dynamics and collision geometry are not expected to play a role. In the multiplicity range where the e⁺e^- results are precise, ridge yields in pp collisions are substantially larger than those observed in e⁺e^- annihilations, indicating that the processes involved in e⁺e^- annihilations do not significantly contribute to the emergence of long-range correlations in pp collisions.

Fig. 11Full-screen View

(Color online) Two-particle per-trigger yield measured for charged track pairs within multiplicity range 32 < N_ch < 37. Jet-fragmentation peak has been truncated for better visibility. [57]

Fig. 12Full-screen View

(Color online) Ridge yield as a function of multiplicity, compared to the upper limits on the ridge yield in e⁺e^- collisions. [57]

The study of nuclear structure in heavy-ion collisions has drawn extensive attention in recent years. Pearson correlations between mean transverse momentum [p_T] and v₂ (v₃) are measured as a function of centrality in Pb–Pb (spherical) and Xe–Xe (deformed) collisions at 5.02 and 5.44 TeV, respectively, in ALICE [58, 59]. The positive correlations of $\rho \left(v_2^2\mathrm{,}[p_{\text{T}}]\right)$ and $\rho \left(v_3^2\mathrm{,}[p_{\text{T}}]\right)$, along with the negative higher-order correlation, are well explained by hydrodynamic models with IP-Glasma initial conditions. This suggests that geometric effects in the initial state play a significant role. The data obtained from Xe–Xe collisions provide a novel avenue for investigating nuclear structure through relativistic heavy-ion collisions at the LHC. Further studies can be found in [60].

Heavy-ion collisions generate extremely strong electromagnetic fields, predominantly caused by spectator protons. These fields are estimated to reach magnitudes of 10¹⁸-10¹⁹ Gauss within the first 0.5 fm of the collision at LHC energy levels. In Ref. [61, 62], such strong electromagnetic fields are probed through charge-dependent directed flow (v₁) [63] in Pb–Pb collisions at $\sqrt{s_{\text{NN}}}$ = 5.02 TeV. The difference in v₁ between positively and negatively charged hadrons exhibits a positive slope with respect to $\eta$. Measurements for D⁰ mesons and their anti-particles reveal a value three orders of magnitude greater than that for charged hadrons. This significant disparity provides new insights into the effects of the strong electromagnetic field, the initial tilt of matter, and the differing sensitivities of charm and light quarks to the early dynamics of heavy-ion collisions. The interplay between the chiral anomaly and intense magnetic (vortical) fields is suggested to generate several chiral anomalous effects [64-67], such as the chiral magnetic effect (CME), chiral magnetic wave (CMW), and chiral vortical effect (CVE). Utilizing various azimuthal- and charge-dependent correlators and methods, the fractions and upper limits (at 95% C.L.) of the CME and CMW have been experimentally extracted with unprecedented precision, as listed in Table 1. Notably, the CMW fraction is a pioneering achievement among all experiments, and a unified background of Local Charge Conservation (LCC) intertwined with collective flow is further proposed to simultaneously interpret the CME and CMW measurements[68]. The chiral vortical effect has also been experimentally measured using Λ-p pairs [69].

In addition to azimuthal correlations, ALICE serves as a novel laboratory for determining the space-time characteristics of relativistic heavy-ion collisions and hadron-hadron interactions through momentum correlations [74, 75]. In Ref. [73], momentum correlations between hyperon–proton pairs are measured in $\sqrt{s}$ = 13 TeV pp and $\sqrt{s_{\text{NN}}}$=5.02 TeV p-Pb collisions with high precision. The influence of strong interactions is examined by comparing experimental data with lattice calculations. In Fig. 13, it is observed that the signal for p- ${\text{Ω}}^{-}$ pairs is up to twice as large as that for p-${\text{Ξ}}^{-}$ pairs. The measured correlations exhibit significant enhancement compared to the Coulomb prediction, indicating the presence of an additional strong attractive interaction. In Ref. [76], p-Λ correlations are measured in $\sqrt{s}$=13 TeV pp collisions. The significance of the coupling between p-Λ and N-∑ is evident from a cusp-like enhancement observed at the corresponding threshold energy. This marks the first direct experimental observation, offering an opportunity to refine theoretical calculations for the coupled $N-{\displaystyle \sum \leftrightarrow }N-\text{Λ}$ system. In another study, Ref. [77] investigates the p-∑⁰ interaction directly, reconstructing ∑⁰ through the Λγ channel. The measured results suggest a shallow strong interaction. In Ref. [78], p-ϕ correlations are obtained from $\sqrt{s}$=13 TeV pp collisions. By fitting the data with theoretical calculations, the scattering length and effective range are extracted. The measured results conclusively exclude inelastic processes in the p-ϕ interaction, providing valuable experimental data for achieving a self-consistent description of the N-ϕ interaction.

Fig. 13Full-screen View

(Color online) Experimental p- ${\text{Ξ}}^{-}$ and p- ${\text{Ω}}^{-}$ correlation functions, indicating presence of additional strong attractive interaction. [73]

In Ref. [80], Kaon-Proton correlations are measured in $\sqrt{s}$=13 TeV pp collisions, both near and above the kinematic threshold. A significant structure is observed around a relative momentum of 58 MeV/c in the correlation function of opposite-charge Kp pairs. This observation, with high statistical significance, represents the first experimental evidence for the opening of the neutral Kn isospin-breaking channel, providing the most precise experimental information to date on the KN interaction.

In the search for the possible Λ-Λ bound state, known as the H-dibaryon, femtoscopic correlations of Λ-Λ pairs are studied in pp and p-Pb collisions [79]. By comparing measured data with model calculations, the scattering parameter space, characterized by the inverse scattering length and effective range, is constrained in Fig. 14. The data reveal a shallow attractive interaction, consistent with findings from hypernuclei studies and lattice computations.

Fig. 14Full-screen View

(Color online) Exclusion plot for the Λ-Λ scattering parameters. Different colors represent the confidence level of excluding a set of parameters. [79]

In addition to strange hadrons, similar measurements have also been extended to charm hadrons. In Ref. [81], momentum correlations of p-D^- and their anti-particle pairs are measured in $\sqrt{s}$=13 TeV collisions. The data are consistent with either a Coulomb-only interaction hypothesis or a shallow N- d strong interaction, contrary to predictions of a repulsive interaction. In Ref. [82], various π- d and K- d pairs are also studied. For all particle pairs, the data can be adequately described by Coulomb interaction alone, and the extracted scattering lengths are consistent with zero. This suggests a shallow interaction between charm and light-flavor mesons.

Three-body nuclear forces are crucial for understanding the structure of nuclei, hypernuclei, and the dynamics of dense baryonic matter, such as in neutron stars. In Ref. [83], ALICE presents the first direct measurement of three-particle correlations involving p-p-p and p-p-Λ systems in pp collisions at $\sqrt{s}$=13 TeV. Using the Kubo formalism, three-particle cumulants are extracted from the correlation functions, where the contribution of the three-particle interaction is isolated by subtracting known two-body interaction terms. A negative cumulant is observed for the p-p-p system, suggesting the presence of a residual three-body effect. Conversely, the cumulant for the p-p-Λ system is consistent with zero, indicating no significant three-particle correlations in this case. Studying correlations between a given particle species and deuterons (d) offers an alternative approach to exploring three-body interactions, as deuterons are composed of a neutron and a proton. In Ref. [84], K⁺- d and p- d femtoscopic correlations are measured. The relative distances at which deuterons and p/ K⁺ are produced are approximately 2 fm. Importantly, only a full three-body calculation that considers the internal structure of the deuteron can adequately explain the observed data. These measurements demonstrate the feasibility of probing three-body correlations at the LHC, providing valuable insights into the complex dynamics involving nuclei and their constituents.

Dileptons, quarkonia and electromagnetic probes

Heavy quarkonia, which are bound states of charm-anticharm (charmonium) or bottom-antibottom (bottomonium) pairs, have been extensively studied in various experiments. Quarkonia serve as essential probes for studying the QGP and its properties. The binding of heavy-quark pairs is affected by the screening of the QCD force due to the high density of free color charges in the QGP, leading to quarkonium dissolution. This concept was first proposed in 1986 [39], with initial studies aiming to link quarkonium suppression directly to the temperature of the deconfined phase. The binding energies of quarkonia, which range from a few MeV to over 1 GeV, suggest a “sequential suppression” with increasing temperature, where strongly bound states persist up to higher dissociation temperatures. In nuclear collisions, varying the QGP temperature by adjusting collision centrality or energy could potentially make quarkonia an ideal thermometer for the medium.

The nuclear modification factor (R_AA) is calculated using the measured yields from Pb–Pb and pp collisions at the same center-of-mass energies. Figure 15 presents the p_T -integrated $J/\psi$ R_AA as a function of N_part in Pb–Pb collisions at $\sqrt{s_{\text{NN}}}$ = 5.02 TeV [85, 86]. $J/\psi$ produced via photo-production processes [87, 88], particularly in peripheral collisions [89, 90], are excluded by applying p_T thresholds greater than 0.15 GeV/c at midrapidity and greater than 0.3 GeV/c at forward rapidity.

Fig. 15Full-screen View

(Color online) p_T -integrated inclusive $J/\psi$ R_AA at midrapidity and forward rapidity, as a function of number of participants in Pb–Pb collisions at $\sqrt{s_{\text{NN}}}$ = 5.02 TeV (upper panel) [86], R_AA at midrapidity are compared with calculations from two microscopic transport models [92, 94] and statistical hadronization model [91](lower panel)

A strong suppression of the $J/\psi$ R_AA is observed in semi-central and central Pb–Pb collisions, especially at forward rapidity. At midrapidity, R_AA exhibits a slight increasing trend from semi-central to central collisions, with R_AA values at midrapidity being slightly larger than those at forward rapidity. This difference is statistically significant, showing a 2.2σ deviation in the 0–10% centrality interval. The larger R_AA in central collisions at midrapidity provides strong evidence for (re)generation effects of $J/\psi$ production at LHC energies [91-93].

The production of the $\psi (\text{2}S)$ was measured in Pb–Pb collisions at $\sqrt{s_{\text{NN}}}$ = 5.02 TeV, with p_T down to 0 for the first time at LHC energies, utilizing the dimuon decay channel at forward rapidity (2.5 < y < 4) by the ALICE experiment [95]. The nuclear modification factors R_AA of $\psi (\text{2}S)$ and $J/\psi$ are compared as a function of N_part in the upper panel of Fig. 16. The R_AA values for $\psi (\text{2}S)$ are systematically lower than those for $J/\psi$. The results are compared with calculations from a microscopic transport model [94] and the statistical hadronization model [91]. The agreement between the data and the transport model is slightly better than with the statistical hadronization model, particularly for $\psi (\text{2}S)$.

Fig. 16Full-screen View

(Color online) p_T -integrated (upper panel) and p_T -differential (lower panel) $\psi (\text{2}S)$ and $J/\psi$ R_AA at forward rapidity in Pb–Pb collisions [95], results are compared with calculations from microscopic transport model [94] and statistical hadronization model [91]

The p_T -differential $\psi (\text{2}S)$ and $J/\psi$ R_AA are compared in the lower panel of Fig. 16. The ALICE results are also compared with similar measurements from CMS, which cover the region of |y| < 1.6 and 6.5 GeV/c < p_T < 30 GeV/c. The CMS data agree with the ALICE measurements within uncertainties in the common p_T range. An increasing trend of R_AA toward low p_T for $\psi (\text{2}S)$, similar to $J/\psi$, is observed, hinting at a (re)generation process of charm and anticharm quarks in $\psi (\text{2}S)$ production. The strong suppression of $\psi (\text{2}S)$ R_AA at high p_T agrees within uncertainties with those of ALICE in the common p_T range.

The polarization of quarkonia in high-energy nuclear collisions can be significantly influenced by the unique conditions within the quark–gluon plasma (QGP). The fast-moving charges of the nuclei generate an intense magnetic field, oriented perpendicular to the reaction plane, which decreases rapidly [96]. Additionally, heavy-quark pair production occurs early in the collision process, and the subsequent evolution into bound states allows the strong magnetic field to potentially affect charmonium polarization. Another factor influencing quarkonia polarization is the orbital angular momentum of the medium [97]. These conditions suggest that both the magnetic field and the vorticity of the QGP can play crucial roles in modifying quarkonium polarization [4].

The measured polarization parameter λθ of the p_T -integrated (2 GeV/c < p_T < 6 GeV/c) inclusive $J/\psi$ as a function of centrality in Pb–Pb collisions at forward rapidity (2.5 < y < 4) via the dimuon decay channels is shown in the upper panel of Fig. 17 [98]. Similar measurements as a function of p_T are shown in the lower panel of Fig. 17. A significant polarization is observed in central and semi-central collisions, with a 3.5σ effect observed. The p_T -dependence indicates that the deviation from zero is more pronounced at lower p_T, with the maximum deviation occurring in the (2 GeV/c < p_T < 4 GeV/c) range during semi-central (30-50%) collisions, where a 3.9σ effect is noted when considering the total uncertainties.

Fig. 17Full-screen View

(Color online) p_T -integrated (upper panel) and p_T -differential (lower panel) polarization parameters of the inclusive $J/\psi$ λθ with respect to the reaction plane in Pb–Pb collisions at forward rapidity via the dimuon decay channels [98]

ALICE also measured the spin alignment of $K^{*0}$ and $\varphi$ mesons in Pb–Pb collisions at midrapidity [99]. The spin matrix element ${\rho }_{00}$ for the polarization parameters is found to be less than 1/3 at low p_T in semi-central Pb–Pb collisions. For $J/\psi$ mesons, the maximum ${\lambda }_{\theta }$ value is approximately 0.2, corresponding to a spin matrix element ${\rho }_{00}\approx 0.25$. Thus, the measured spin matrix elements ${\rho }_{00}$ for $K^{*0}$ and $\varphi$ mesons in Pb–Pb collisions are all less than 1/3. Future theoretical studies on charmonium production, along with experimental improvements and increased integrated luminosity, are essential to confirm and further understand the mechanisms underlying the spin alignment of vector mesons in heavy-ion collisions.

As mentioned earlier, the magnetic field produced by the highly Lorentz-contracted ultra-relativistic heavy-ion collisions can reach magnitudes of up to 10¹⁵ Tesla, potentially giving rise to various exotic phenomena. The measurement of thermal dilepton production from the QGP and the hot hadron gas produced in heavy-ion collisions has long been recognized as a precise and powerful probe for studying the time evolution of the medium’s properties [100]. The first measurement of low-mass ${\text{e}}^{+}{\text{e}}^{-}$ pair production at low p_T in Pb–Pb collisions at $\sqrt{s_{\text{NN}}}$ = 5.02 TeV has been presented [101, 102].

The invariant mass spectra of ${\text{e}}^{+}{\text{e}}^{-}$ pair production are shown in Fig. 18. The yield of ${\text{e}}^{+}{\text{e}}^{-}$ pair production in the range $0.2\text{GeV}/c<p_{\text{T}}<10\text{GeV}/c$ is presented as a function of $m_{\text{ee}}$ for 0–10% central Pb–Pb collisions at $\sqrt{s_{\text{NN}}}$ = 5.02 TeV (upper panel). The measurements are compared with expected contributions from known hadronic sources, specifically the $R_{\text{AA}}^{\text{c}\mathrm{,}\text{b}\to {\text{e}}^{\pm }}$-modified heavy-flavor (HF) cocktail and the $N_{\text{coll}}$-scaled HF cocktail. At low invariant masses ($0.18\text{GeV}/c^2<m_{\text{ee}}<0.5\text{GeV}/c^2$), the ratios indicate a potential excess that is consistent with unity within certain confidence levels. Notably, this excess does not significantly depend on the method used for estimating heavy flavor. The contribution from $\rho$ mesons, excluding medium effects, accounts for approximately 18% of the total hadronic yield; however, thermally produced ${\text{e}}^{+}{\text{e}}^{-}$ pairs from $\rho$ mesons are expected to be significant. In the intermediate mass range ($1.2\text{GeV}/c^2<m_{\text{ee}}<2.6\text{GeV}/c^2$), the data are better described by the modified HF cocktail, although this region still faces considerable uncertainties. The lower panel presents the non-central (70–90%) and semi-central (50-70%) Pb–Pb collisions at $\sqrt{s_{\text{NN}}}$ = 5.02 TeV, measured within the ALICE acceptance at midrapidity and for (p_T > 0.2 GeV/c). The yields of the produced ${\text{e}}^{+}{\text{e}}^{-}$ pairs are compared to the expected ${\text{e}}^{+}{\text{e}}^{-}$ production from hadronic sources, represented as “cocktails”. A clear excess is observed relative to the hadronic cocktail in both centrality classes, with enhancement factors being larger in the (70-90%) collisions compared to the (50–70%) collisions. The hadronic cocktail contribution is subtracted from the inclusive ${\text{e}}^{+}{\text{e}}^{-}$ pairs. Contributions from thermal dielectrons, arising from both the partonic and hadronic phases, are estimated using an expanding thermal fireball model that incorporates an in-medium broadened p spectral function [103, 104]. It is anticipated that thermal radiation from the medium will be at least an order of magnitude smaller than the measured ${\text{e}}^{+}{\text{e}}^{-}$ pairs.

Fig. 18Full-screen View

(Color online) Dielectron $m_{{\text{e}}^{+}{e}^{-}}$ -differential yields comparison with expected ${\text{e}}^{+}{\text{e}}^{-}$ contributions from hadronic production decays in Pb–Pb collision at $\sqrt{s_{\text{NN}}}$ = 5.02 TeV in 0–10% centrality interval (upper panels), with similar comparisons in 50–70% and 70–90% centrality classes (lower panels) [101, 102]

Heavy flavor probes

In ultra-relativistic heavy-ion collisions, hard scatterings involving parton constituents of nucleons can produce a variety of energetic final states, collectively referred to as “hard probes.” Hard probes are energetic partons created in high momentum-transferred (high-Q²) partonic scattering processes during the early stage of heavy-ion collisions. Since their formation time is shorter than the QGP medium’s lifetime, they experience the entire medium evolution. Due to the high momentum and short-wavelength characteristics of hard probes, their interactions with the medium constituents are highly sensitive to the microscopic structure and quasi-particle nature of the medium. This makes hard probes a valuable tool for providing a “tomography” of the medium across a wide virtuality (wavelength) range. The high-Q² scale allows the production cross sections of hard probes to be calculated with controlled and improvable accuracy using perturbative QCD (pQCD) tools. Furthermore, the interactions between hard probes and the QGP medium can be modeled starting from the pQCD formulation of elementary collisions or transport theory, providing a firm conceptual foundation for such modeling approaches. HF quarks, jets, and photons are all examples of hard probes that have been extensively studied by ALICE during Runs 1 and 2 data collection.

For heavy quarks, such as charm and beauty quarks, the high-Q² scale is imparted by their large masses ($m_{\text{charm}}\simeq 1.5$ GeV/c² and $m_{\text{beauty}}\simeq 4.5$ GeV/c²) [105], which are much larger than both Λ_QCD and the medium temperature [40]. Their production, even at low transverse momentum $p_{\text{T}}$, is predominantly governed by early stage hard partonic scatterings. The contribution from medium evolution and additional thermal production is negligible. Therefore, heavy quarks serve as self-normalized probes of the QCD medium.

When propagating through the QGP medium, heavy quarks interact with the medium constituents via both elastic (collisional) and inelastic (induced radiative) processes, leading to in-medium energy loss at low and high p_T, respectively [106, 107]. This energy loss is experimentally explored by measuring the nuclear modification factor R_AA. In the absence of QGP formation in pp collisions, R_AA = 1 if AA collisions were simply a superposition of nucleon-nucleon collisions. However, when a heavy quark deposits most of its energy into the QGP medium, it may begin to participate in the medium’s hydrodynamic expansion, potentially approaching thermalization.

The ALICE experiment measures fully reconstructed open HF hadrons from their hadronic decays at midrapidity (|y| < 0.5) [108-116]. In addition, open HF production is measured using semi-electronic [117-120] and semi-muonic decays [121-125] at midrapidity (|y|<0.8 for low- and intermediate-p_T and |y|<0.6 for high-p_T) and forward rapidity (2.5 < y < 4), respectively. The semi-electronic decays are also used for the partial reconstruction of charmed baryons [113, 126, 127]. Furthermore, beauty production is measured via non-prompt $J/\psi$ from the decay mode $\text{B}\to J/\psi +X$ [128-130] and non-prompt D mesons from the decay mode $\text{B}\to \text{D}+X$ [131, 132].

The left and right panels of Fig. 19 show, respectively, R_AA and the second-order anisotropy flow (elliptic flow) coefficient v₂ as a function of p_T for prompt D mesons measured at midrapidity in central (0-10%) and semi-central (30-50%) Pb-Pb collisions at $\sqrt{s_{\text{NN}}}=5.02$ TeV with ALICE [133, 134]. A significant suppression, up to a factor of five, is observed in the yields of D mesons in the intermediate- and high-p_T regions in the most central 10% of Pb-Pb collisions, indicating that charm quarks undergo strong in-medium energy loss in the QGP. Furthermore, a positive v₂ of D mesons is observed at intermediate p_T in the 30-50% semi-central collisions, indicating that charm quarks participate in the collective motion of the QGP as a result of their substantial energy deposition in the medium. At low- and intermediate-p_T, i.e., $p_{\text{T}}\lesssim 10$ GeV/c, charm quarks exchange energy and momentum through multiple soft and incoherent collisions within the hydrodynamically expanding medium. The interaction of charm quarks with the medium is typically treated using a diffusion approach based on Fokker-Planck or Langevin dynamics, which describes their behavior in terms of Brownian motion in the QGP. Hence, the coupling between the medium and charm quarks can be expressed by the spatial diffusion coefficient D_s, which is almost independent of the quark mass and encodes the transport properties of the medium [107, 135, 136]. Furthermore, D_s is proportional to the relaxation time τ_Q of heavy particles, i.e., τ_Q = (m_Q/T)D_s, where m_Q and T denote the heavy-quark mass and medium temperature, respectively.

Fig. 19Full-screen View

(Color online) p_T-differential R_AA (left) and v₂ (right) of prompt D mesons measured, respectively, in 0-10% and 30-50% centrality classes at midrapidity in Pb-Pb collisions at $\sqrt{s_{\text{NN}}}=5.02$ TeV by ALICE [133, 134]

In Fig. 19, the measurements are also compared with model calculations based on charm-quark transport in a hydrodynamically expanding QGP. All models are qualitatively in agreement with the data, including the triangular flow coefficient v₃ of D mesons [133]. Although some tension is observed, particularly at low-p_T, models that agree with data at the level χ²/ndf < 2 yield a value 1.5 < 2π D_sT < 4.5, where T is the temperature at the critical point of the QCD deconfinement phase transition, $T_{\text{c}}\simeq 155$ MeV [137, 138]. By adopting m_charm = 1.5 GeV/c², the corresponding charm-quark relaxation time ${\tau }_{\text{charm}}$ is estimated to lie in the range 3 < τ_charm < 9 fm/c. These values are similar in magnitude to the estimated lifetime of the QGP, ${\tau }_{\text{QGP}}\simeq 10$ fm/c at LHC energies [43], suggesting that charm quarks may fully thermalize in the QGP medium created at LHC energies.

It is worth noting that R_AA [121, 124] and v₂ [122] of open HF decay muons measured at forward rapidity agree with those of prompt D mesons at midrapidity within uncertainties at low- and intermediate-p_T, where the muons are primarily dominated by charm-hadron decays. This indicates that charm quarks undergo strong interactions and thermalize in the QGP medium over a wide rapidity range. The complementary measurements at forward rapidity provide significant constraints on the modeling of the longitudinal dependence of QGP transport properties [139]. In addition, the R_AA [124] measurements of open heavy flavors at forward rapidity have much higher precision than those at midrapidity in the high p_T, providing further constraints on the medium-induced gluon radiation behavior of beauty quarks.

To further explore the transport properties of beauty quarks in the QGP medium, non-prompt D mesons are measured at midrapidity by ALICE. The left and right panels of Fig. 20 show, respectively, the measurements of p_T-differential R_AA and v₂ of non-prompt D⁰ mesons in central (0-10%) and semi-central (30-50%) Pb-Pb collisions at $\sqrt{s_{\text{NN}}}=5.02$ TeV with ALICE [132, 140]. The results are compared with the corresponding measurements of prompt D mesons [133, 134]. Similar to prompt D mesons, a significant suppression is observed in the yield of non-prompt D⁰ mesons at intermediate and high p_T in the most central 10% of the Pb-Pb collisions, indicating that beauty quarks also undergo substantial in-medium energy loss in the QGP. Compared to prompt D mesons, an enhancement in the non-prompt D⁰-meson R_AA illustrates the mass-dependent in-medium energy loss of heavy quarks, resulting from the dead-cone effect [141], which causes beauty quarks to experience less energy loss in the medium relative to charm quarks.

Fig. 20Full-screen View

(Color online) p_T-differential R_AA (left) and v₂ (right) of non-prompt D⁰ mesons measured, respectively, in 0-10% and 30-50% centrality classes at midrapidity in Pb-Pb collisions at $\sqrt{s_{\text{NN}}}=5.02$ TeV by ALICE [132, 140]. Results are compared with the corresponding measurement of prompt D mesons [133, 134]

Consistent with the large yield suppression, a positive v₂ is observed for non-prompt D⁰ mesons at intermediate p_T in 30-50% semi-central collisions, with a significance of 2.7 standard deviations (σ). The measured v₂ of non-prompt D⁰ mesons is lower than that of prompt D mesons, with a 3.2σ significance in the 2 GeV/c <p_T<8 GeV/c range. Given that the spatial diffusion coefficient D_s is independent of heavy-quark mass and that m_beauty is approximately three times larger than m_charm, the beauty-quark relaxation time τ_beauty is likely comparable to or even longer than the QGP lifetime τ_QGP at the LHC. This suggests that beauty quarks are less thermalized in the QGP medium than charm quarks, leading to the observed smaller v₂ for non-prompt D⁰ mesons compared to prompt D mesons at intermediate p_T. At high p_T, the measured v₂ of non-prompt D⁰ mesons and prompt D mesons appears consistent, reflecting the interplay between path-length-dependent heavy-quark in-medium energy loss and the evolution and density fluctuations of the QGP medium.

The degree of thermalization of charm and beauty quarks as they interact with the QGP medium not only leads them to participate in the collective motion of the medium but also suggests their hadronization through recombination with quarks and di-quark pairs in the medium. Recombination is expected to influence the p_T distributions and the abundances of different HF hadron species in AA collisions compared to those in pp collisions [142]. Specifically, if heavy quarks hadronize via recombination, the yield of charm and beauty hadrons containing strange-quark content (e.g., $D_{\text{s}}^{+}$ and $B_{\text{s}}^0$ mesons) relative to non-strange hadrons is expected to be larger in AA collisions compared to pp collisions, because of the enhancement of strange-quark production in the QGP medium [143, 144]. Moreover the production of baryons relative to mesons is expected to be enhanced at intermediate-p_T, i.e., $2\lesssim p_{\text{T}}\lesssim 8$ GeV/c [145-150]. In addition, the collective radial expansion of the QGP medium, which determines a flow-velocity profile common to the thermalized particles, could also increase the baryon-to-meson yield ratio at intermediate p_T [148-150]. A precise description of the hadronization process in the hot nuclear matter is crucial to understanding the transport properties of the QGP [151].

The left panel of Fig. 21 shows the p_T-differential ${\text{Λ}}_{\text{c}}^{+}$/D⁰ yield ratio measured in midrapidity in central (0-10%) and semi-central (30-50%) Pb-Pb collisions at $\sqrt{s_{\text{NN}}}=5.02$ TeV by ALICE. The measurements are compared with those obtained from pp collisions at the same binary center-of-mass collisions [153]. The ratios increase from pp to mid-central and central Pb-Pb collisions for 4 < p_T < 8 GeV/c, with a significance of 2.0σ and 3.7σ, respectively. This trend is qualitatively consistent with charm-quark transport in an expanding medium using the Langevin approach and hadronization primarily via coalescence in Pb-Pb collisions [149, 156]. The right panel of Fig. 21 reports the p_T-differential R_AA double ratio of non-prompt $D_{\text{s}}^{+}$ mesons to non-prompt D⁰ mesons for the 0-10% and 30-50% centrality intervals in Pb–Pb collisions at $\sqrt{s_{\text{NN}}}=5.02$ TeV measured by ALICE [154]. Measuring non-prompt $D_{\text{s}}^{+}$ mesons alongside non-prompt D⁰ mesons provides the potential to shed light on the beauty-quark hadronization mechanisms in the QGP medium, as approximately 50% of non-prompt $D_{\text{s}}^{+}$ mesons are produced from strange-beauty meson $B_{\text{s}}^0$ decays in pp collisions [105, 131]. The double ratio measured in the most central 10% of collisions suggests a possible enhancement relative to unity in the range 4 < p_T < 12 GeV/c. The rise at low p_T may result from an enhanced production of strange-beauty mesons compared to non-strange-beauty mesons in heavy-ion collisions. This is expected in scenarios where the abundance of strange quarks thermally produced in the QGP medium and the dominance of beauty-quark hadronization via recombination with surrounding quarks in a strangeness-enriched environment play a significant role. The TAMU model [155], which incorporates beauty-quark hadronization via recombination with light quarks from the medium, describes the data within experimental uncertainties.

Fig. 21Full-screen View

(Color online) Left: ${\text{Λ}}_{\text{c}}^{+}$/D⁰ ratio measured at midrapidity in central (0-10%) and semi-central (30-50%) Pb–Pb collisions at $\sqrt{s_{\text{NN}}}=5.02$ TeV by ALICE [152]. The measurements are compared with those obtained from pp collisions at the same binary center-of-mass energy [153]. Right: p_T-differential double ratio of R_AA between non-prompt $D_{\text{s}}^{+}$ and D⁰ measured at midrapidity for 0-10% and 30-50% centrality intervals in Pb–Pb collisions at $\sqrt{s_{\text{NN}}}=5.02$ TeV by ALICE [154]. The measurements are compared with TAMU model predictions [155]

An accurate interpretation of all the aforementioned measurements in heavy-ion collisions, which is crucial for characterizing the properties of the QGP medium, depends on a reference system in which the QGP medium is not formed. Traditionally, small-system collisions (e.g., pp and p-Pb), due to their dilute partonic environment, serve as the baseline for AA collision studies. In addition, measuring HF production in pp collisions provides a fundamental test for pQCD calculations in the TeV domain [157, 158].

The production cross sections of $\text{c}\overline{\text{c}}$ [159] and $\text{b}\overline{\text{b}}$ [128, 131, 160-162] at midrapidity in pp collisions have been measured by ALICE. For the $\text{c}\overline{\text{c}}$ measurements, the results are higher than the upper edge of pQCD-based FONLL and NNLO calculations, though compatible within approximately ～1σ of the experimental uncertainties. The measured $\text{b}\overline{\text{b}}$ production cross sections are found to be compatible with FONLL and NNLO calculations. It is worth noting that the uncertainties in the $\text{c}\overline{\text{c}}$ measurements are significantly smaller than those in the theoretical predictions, thereby imposing stricter constraints on the theoretical calculations. Similar observations arise from the ($p_{\text{T}}\mathrm{,}y$)-double-differential comparison of FONLL predictions with the cross sections of muons from the semi-leptonic decays of charm and beauty hadrons measured at forward rapidity [163, 164]. These measurements set additional constraints for pQCD calculations in a kinematic region important for probing parton distribution functions (PDFs) at low Bjorken-x values, down to approximately ～10^-5.

The mentioned theoretical calculations are based on pQCD factorization approaches [170, 171], where fragmentation functions are typically parametrized from measurements performed in e^-e⁺ or e_p collisions, assuming that the hadronization of heavy quarks into hadrons is a universal process across different colliding systems. However, this assumption may be violated by higher-twist effects or other factors related to heavy-quark kinematics and the underlying event in pp collisions [172-174]. This effect is observed in recent measurements of charmed meson-to-baryon yield ratios at midrapidity in pp collisions at various collision energies for ${\text{Λ}}_{\text{c}}^{+}/D^0$ [153, 175, 112], ${\sum }_{\text{c}}^{\mathrm{0,}++}/D^0$ [176], ${\text{Ξ}}_{\text{c}}^{+\mathrm{,0}}/D^0$ [126, 127, 113], and ${\text{Ω}}_{\text{c}}^0/D^0$ [177]. The ALICE results reveal higher baryon-to-meson cross section ratios at low-p_T compared to e^-e⁺ and e_p collisions. Notably, the ${\sum }_{\text{c}}^{\mathrm{0,}++}$ and ${\text{Ξ}}_{\text{c}}^{+\mathrm{,0}}$ cross sections have been measured for the first time in hadronic collisions. A consequence of the significant difference between the charmed baryon-to-meson yield ratios measured in pp and e^-e⁺ and e_p collisions is that the charm-quark fragmentation fractions, $f(\text{c}\to {\text{h}}_{\text{c}})$, i.e., the probabilities of a charm-quark hadronizing into a given charmed hadron species ${\text{h}}_{\text{c}}$, obtained in pp collisions differ from those estimated from e^-e⁺ and e_p data, as presented in the left panel of Fig. 22. In addition, $f\left(\text{c}\to {\text{h}}_{\text{c}}\right)$ is also extracted from p-Pb collisions by ALICE [178]. The results are nearly identical to those from pp collisions, indicating no significant modification of charm-quark hadronization between the two colliding systems, despite the larger system size and higher charged-particle multiplicity density in p-Pb collisions. These observations provide evidence that the assumption of universality (colliding-system independence) of parton-to-hadron fragmentation functions is not valid for charmed hadron production.

Fig. 22Full-screen View

(Color online) Left: charm-quark fragmentation fractions $f(\text{c}\to {\text{h}}_{\text{c}})$ measured at midrapidity in pp collisions at $\sqrt{s}=5.02$ TeV and 13 TeV by ALICE [165]. The results are compared with those obtained from e^-e⁺ and ep collisions [166]. On the right: p_T-differential v₂ coefficient of muons, measured using the two-particle correlation (2PC) method at forward rapidity in high-multiplicity p-Pb collisions at $\sqrt{s_{\text{NN}}}=8.16$ TeV by ALICE [167] is presented. The measurements are compared with AMPT [168] and CGC [169] calculations

Furthermore, the measurements in p-Pb collisions are crucial for constraining cold nuclear matter (CNM) effects [179], which include nuclear modified PDFs (nPDFs), multiple scatterings in nucleons that collide with more than one other nucleon, the Cronin effect, parton energy loss in CNM, and absorption of produced hadrons by the nucleus. ALICE measures the nuclear modification factors of open HF particles in p-Pb collisions for D mesons [180], ${\text{Λ}}_{\text{c}}^{+}$ [181], and ${\text{Ξ}}_{\text{c}}^0$ [182] baryons, as well as open HF hadron decay electrons [118] at midrapidity and open HF decay muons [123] at forward rapidity. The measurements of open HF hadron decay muons at forward rapidity, in conjunction with the measurement of W^±-boson production [183] in the same rapidity region, also provide important constraints on nPDFs at Bjorken-x values down to 10^-6. In addition, the nuclear modification factors for beauty-quark production in p-Pb collisions have been measured by ALICE for beauty-hadron decay electrons [184] and b-tagged jets [185] at midrapidity. All these measurements are consistent with predictions that consider only the CNM effects, within both experimental and theoretical uncertainties.

Up to now, all the aforementioned observations in small-system collisions indicate that such systems can be considered as baseline references, in which the conditions to form the QGP cannot be reached. Surprisingly, as illustrated in the right panel of Fig. 22, a non-zero v₂ coefficient for open HF hadron decay muons—considered emblematic signatures of QGP formation—is observed at forward rapidity in high-multiplicity p–Pb collisions at $\sqrt{s_{\text{NN}}}=8.16\text{ TeV}$ by ALICE [167]. A similar observation is also found at midrapidity for open HF hadron decay electrons [186]. The measurements are compared with AMPT [168] and CGC [169] calculations. In the AMPT model, the anisotropy is derived from the escape mechanism via partonic interactions. On the other hand, the CGC calculations are based on the dilute-dense formalism, where interactions between partons from the proton projectile and dense gluons inside the target Pb nucleus at the early stage of the collision generate azimuthal anisotropies. For muons measured in the ALICE forward muon spectrometer, the HF contribution is the primary source for p_T > 2 GeV/c. Despite CGC calculations overestimating the measurements in the first few data p_T intervals, the two predictions generally agree with the observed anisotropy within experimental uncertainties. The model comparison suggests that either initial- or final-state partonic interactions may generate the hydrodynamic-like azimuthal anisotropy in momentum space for HF particles. Besides, the existence of small QGP droplets at high multiplicity in small-system collisions remains a topic of debate.

In the future, the high-multiplicity LHC project for ALICE during LHC Run 3 and Run 4, along with the ALICE 3 detector upgrade project for LHC Run 5 and beyond (see Sect. 3), will be crucial for revealing the origins of the observed non-universality in charm-quark hadronization and the QGP-like effects observed in small-system collisions.

Jets

Jets play a crucial role in ultra-relativistic heavy-ion collisions, serving multiple key functions. They help identify the initial momentum scale of hard scatterings, especially for photons and other colorless probes. Moreover, jets offer valuable insights into the interactions within the dense QCD medium, particularly those involving quarks and gluons, which carry QCD color charge. By studying jet substructure, HF quarks, and the highest transverse-momentum jets, researchers can thoroughly explore interactions within the QCD medium across various topologies and kinematic ranges.

In Fig. 23, the nuclear modification factors are depicted for R = 0.6 (left) and the double ratio of jet nuclear modification factors between R = 0.6 and R = 0.2 (right), presented for 0–10% central Pb–Pb collisions and compared to theoretical calculations incorporating jet quenching [187]. The double ratio R_AA is a critical measure for evaluating the R-dependence of energy loss in jets. Values below unity indicate greater suppression for jets with larger R, values at unity suggest no R-dependence or a balancing of effects, and values above unity imply less suppression for larger R jets. In 0–10% central collisions, the $R_{\text{AA}}^{0.6/0.2}$ ratio shows suppression below unity at lower jet p_T values, indicating a potential R-dependence within the uncertainties.

Fig. 23Full-screen View

(Color online) Nuclear modification factors for R = 0.6 (left) and double ratio of jet nuclear modification factors between R = 0.6 and R = 0.2 (right), shown at central 0–10% of Pb–Pb collisions compared to theoretical calculations incorporating jet quenching [187]

Event-shape engineering (ESE) is an experimental technique that classifies events based on their anisotropies using the magnitude of the reduced flow vector, providing a novel method to constrain the path-length dependence of jet energy loss. To investigate the event-shape dependence, events were categorized based on the magnitude of the reduced flow vector q₂, measured with the forward detector V0C. Figure 24 shows the ratio of out-of-plane to in-plane jet yields for the q₂-small and q₂-large event classes, focusing on jets with R=0.2 in mid-central 30-50% Pb–Pb collisions at $\sqrt{s_{\text{NN}}}$=5.02 TeV [188]. The observed ratios are significantly below unity, indicating that jets lose more energy on average when traveling out-of-plane compared to in-plane. This finding supports the notion that the extent of jet energy loss is influenced, at least partially, by the path length through the medium.

Fig. 24Full-screen View

(Color online) Ratios of out-of-plane to in-plane charged-particle jet yields for q₂-large and q₂-small event classes in Pb–Pb collisions at $\sqrt{s_{\text{NN}}}=5.02$ TeV [188]

Medium-induced yield modification is measured by I_AA(p_{T,ch jet})=Δ_recoil(Pb-Pb)/Δ_recoil(pp), which represents the ratio of the Δ_recoil(p_T,jet) distributions measured in Pb–Pb and pp collisions. Figure 25 presents the I_AA(p_{T,ch jet}) distributions measured for R=0.4 with the default TT_sig selection (left panel) and with varied TT_sig selections (right panel) in central Pb–Pb collisions. The I_AA(p_{T,ch jet}) distributions show a notable dependence on p_{T,ch jet}. For R=0.4, JEWEL (recoils on) exhibits a significant increase in I_AA(p_{T,ch jet}) toward low p_{T,ch jet} for p_{T,ch jet}<20 GeV/c, mirroring the trend in the data for R=0.4. Overall, JETSCAPE most accurately describes both the magnitude and p_{T,ch jet} dependence of I_AA(p_{T,ch jet}) in the range p_{T,ch jet}<20 GeV/c. The rising trend in the data toward low p_{T,ch jet} for p_{T,ch jet}<20 GeV/c is captured by both the Hybrid Model and JEWEL, but only with the inclusion of medium-response effects [190, 189]. Figure 25 (right) displays the I_AA(p_{T,ch jet}) distribution for R=0.4 measured for several $p_{\text{T}}^{\text{trig}}$ intervals used in the TT_sig event selection. A higher $p_{\text{T}}^{\text{trig}}$ threshold corresponds to larger $\tilde{z}$, where the assumptions underlying the surface-bias picture may better apply. The results indicate that as the lower $p_{\text{T}}^{\text{trig}}$ bound is raised, the rate of increase in I_AA(p_{T,ch jet}) at large p_{T,ch jet} diminishes.

Fig. 25Full-screen View

(Color online) I_AA(p_{T,ch jet}) from Δ_recoil(p_{T, jet}) distributions measured for R = 0.4 with default TT_sig selection (left) and with varied TT_sig selections (right) in central Pb–Pb collisions [189]

Figure 26 presents the first observation of medium-induced jet acoplanarity broadening in the QGP. The broadening is significant in the range of 10 GeV/c < p_Tjetch<20 GeV/c for R=0.4 and 0.5, but it is negligible for R=0.2, and at larger p_{Tch, jet} for all R. This rapid transition in the shape of the acoplanarity distribution as a function of both p_{T,ch jet} and R is striking. Possible mechanisms for generating acoplanarity broadening include jet scattering from QGP quasi-particles, medium-induced wake effects, and jet splitting, where medium-induced radiation from a high-p_{T,ch jet} jet is reconstructed at low p_{T,ch jet} with a large deviation from Δ(phi)～π [190, 189].

Fig. 26Full-screen View

(Color online) I_AA(Δ(phi)) for R=0.2, 0.4 and 0.5, for intervals in recoil p_{T,ch jet}: [10, 20], [20, 30], and [30, 50] GeV/c. Predictions from JEWEL are also shown [190]

Jet quenching, a phenomenon associated with the formation of QGP in large nuclear systems, is anticipated to occur in smaller systems, albeit with diminished effects. Currently, there is no definitive evidence, beyond experimental uncertainties, of jet quenching in small systems. This raises the question of whether the observed collective effects in these systems genuinely stem from QGP formation or from other mechanisms. Further investigations are essential to search for jet quenching effects in small systems and to address this unresolved issue.

To investigate the p_T dependence of normalized jet production as a function of self-normalized charged-particle multiplicity, Fig. 27 displays the self-normalized jet yields across four selected jet p_T intervals for resolution parameters R=0.3, 0.5, and 0.7. The data are also compared with PYTHIA8 predictions [191]. The measured jet production ratios in central rapidity exhibit an increase with multiplicity, mirroring earlier findings for identified particles using the forward multiplicity V0 estimator. However, the increase is less pronounced for the lowest jet p_T in the highest multiplicity interval. Current Monte Carlo (MC) event generators can predict the rising trend but fail to accurately describe the absolute yields, particularly in the highest multiplicity class.

Fig. 27Full-screen View

(Color online) Comparison of self-normalized jet yields as a function of self-normalized charged-particle multiplicity in four selected jet p_T intervals ($5\text{GeV}/c\le p_{\text{T,jet}}^{\text{ch}}<7\text{GeV}/c$, $9\text{GeV}/c\le p_{\text{T,jet}}^{\text{ch}}<12\text{GeV}/c$, $30\text{GeV}/c\le p_{\text{T,jet}}^{\text{ch}}<50\text{GeV}/c$, and $70\text{GeV}/c\le p_{\text{T,jet}}^{\text{ch}}<100\text{GeV}/c$) for given jet radii: a) R = 0.3, b) R = 0.5, c) R = 0.7 between data and PYTHIA8 predictions [191]

Figure 28 presents fully corrected distributions of Δ_recoil (p_{T,ch jet}) and Δ_recoil (Δ(phi)) measured in minimum bias (MB) and high multiplicity (HM)-selected pp collisions at $\sqrt{s}$= 13 TeV, alongside calculations from various models [192]. The comparison of MB and HM Δ_recoil (p_{T,ch jet}) distributions shows a yield suppression in HM collisions that remains largely independent of p_T,jet, although there is a slight indication of a harder recoil jet spectrum for HM events. The Δ_recoil (Δ(phi)) distributions reveal that jet yield suppression in HM events primarily occurs in the back-to-back configuration. While the total yield is reduced, the azimuthal distribution is broadened. This broadening may result from jet quenching, where medium-induced jet scattering is more prevalent in HM events. However, PYTHIA 8 particle-level distributions also show jet yield suppression and azimuthal broadening in HM-selected events, accurately matching the measured distributions. Since PYTHIA 8 does not account for jet quenching, this suggests that jet quenching is not the dominant factor causing the observed broadening in the data.

Fig. 28Full-screen View

(Color online) Fully corrected Δ_recoil distributions measured in MB and HM-selected events in pp collisions at $\sqrt{s}=13$ TeV. Left panel: Δ_recoil (p_{T,ch jet}) in |Δ(phi)-π|<0.6; middle and right panels: Δ_recoil (Δ(phi)) for 20 GeV/c <p_{T,ch jet}<40 GeV/c and 40 GeV/c <p_{T,ch jet}<60 GeV/c [192]

Moreover, the count of emissions produced by the charm quark that meet the soft drop criterion, represented as n_SD, is determined by examining all branch splittings involving the D⁰ meson. This analysis reveals a significant correlation with the number of perturbative emissions originating directly from the charm quark.

The initial measurement, correlating with the charm-quark splitting function, is depicted through the n_SD distribution illustrated in Fig. 29. This distribution pertains to charm jets identified by a prompt D⁰ meson within the transverse momentum range 15 GeV /c≤p_T,jet<30 GeV /c [193]. Compared to inclusive jets, the n_SD distribution for charm-tagged jets exhibits a noticeable shift toward smaller values. This observation suggests that, on average, charm quarks emit fewer gluons with sufficiently high p_T to satisfy the soft drop condition during the showering process, in contrast to light and massless partons. This behavior aligns with expectations arising from the presence of a “dead cone” effect specific to charm quarks, which leads to a steeper fragmentation pattern for charm quarks relative to light quarks and gluons.

Fig. 29Full-screen View

(Color online) The n_SD distributions of prompt D⁰ -tagged jets compared to those of inclusive jets for 15 GeV/c ≤ p_T,jet < 30 GeV/c in pp collisions at $\sqrt{s}$ = 13 TeV [193]

The observable utilized to detect the dead cone involves forming the ratio of the splitting angle (θ) distributions between jets tagged with D⁰-mesons and inclusive jets, grouped into bins of E_Radiator. Expressing this ratio in terms of the logarithm of the inverse of the angle is appropriate, as at leading order, the QCD likelihood for a parton to split is proportional to ln(1/θ)ln(k_T).

Figure 30 presents measurements of R(θ) in three intervals of radiator energy associated with charm quarks: 5 GeV < E_Radiator < 10 GeV, 10 GeV < E_Radiator < 20 GeV, and 20 GeV < E_Radiator < 35 GeV [194]. A pronounced reduction in the occurrence of small-angle splittings is evident in jets tagged with D⁰ mesons compared to the general jet sample. Each plot includes a baseline corresponding to scenarios without a dead cone for every MC generator (dashed lines). The discrepancy between the measured data points and the no dead-cone limit directly illustrates the presence of a dead cone, where emissions from charm quarks are suppressed. This suppression becomes more pronounced with lower radiator energies, consistent with the anticipated inverse relationship between the dead-cone angle and radiator energy.

Fig. 30Full-screen View

(Color online) Nuclear modification factors for R = 0.6 (left) and double ratio of jet nuclear modification factors between R = 0.6 and R = 0.2 (right), shown for central 0–10% of Pb-Pb collisions compared to theoretical calculations incorporating jet quenching [194]