Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (2025)

When heavy atomic nuclei collide at relativistic speeds, a transformation occurs, giving rise to an exotic state of matter with a temperature above several trillion kelvin and known as the quark–gluon plasma (QGP) [14]. In this realm of extreme temperatures, quarks and gluons break free from their confined existence inside hadrons, traversing long distances (e.g. several fm) compared to the size of individual nucleons. The emergence of the QGP represents a fundamental prediction of quantum chromodynamics (QCDs) [5, 6], the theory that elucidates the nature of the strong force. More remarkably, this strongly interacting QGP matter is found to exhibit the characteristics of an almost 'perfect liquid' with little frictional momentum dissipation [710]. Its collective dynamics and macroscopic properties are well described by the principles of nearly ideal relativistic hydrodynamics.

The equation of state (EoS) reveals the underlying fundamental degrees of freedom of a substance and is an invaluable tool to infer how the substance will respond to changes in its energy density. In fluid-like environments, the study of sound modes arising from longitudinal compression provides a means to determine the corresponding speed of sound, denoted as Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (1). This parameter, whose square is defined as the rate of pressure P change in response to variations in energy density ε, Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (2) [11], plays a pivotal role in characterizing the nature of the medium under investigation and in constraining models of corresponding EoS. The exploration of the sound wave propagation in strongly correlated systems, ranging from neutron stars to ultracold atomic gases [12, 13], has garnered significant interest in recent years. Various methodologies have been proposed to experimentally extract the speed of sound in a QGP fluid [1418], offering a direct means to constrain the QCD EoS. Notably, constraints on the speed of sound in hot QCD matter have been inferred through a comparison of relativistic nuclear collision data with theoretical models within a Bayesian framework [15]. Recently, an effort to directly extract Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (3) in the QGP phase was made by establishing a connection to an effective static, uniform fluid system [16]. That work was based on only two independent measurements of the charged-particle multiplicity density and mean transverse momentum (Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (4)) in lead–lead (PbPb) collision data from the ALICE experiment at center-of-mass energies per nucleon pair Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (5) and Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (6), and yielded a value of Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (7) in natural units at a temperature of Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (8) MeV. This result is in line with lattice QCD predictions, albeit subject to significant experimental uncertainties.

To increase the precision by which the speed of sound can be determined, a new hydrodynamic probe was later proposed in [17] utilizing the multiplicity dependence of mean pExtracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (9) measurements at a fixed Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (10). This innovative technique makes use of 'ultra-central' collisions in which the ions overlap almost entirely, i.e. collide at a very small impact parameter (b). A conceptual representation of this probe is illustrated in figure 1. The impact parameter of a heavy ion collision determines the size of the nuclear overlap region (system size), which is strongly correlated with the energy and entropy deposited in the initial state and the number of emitted charged particles in the final state ('multiplicity', Nch). As the impact parameter decreases and collisions become increasingly central, both the system size and deposited energy increase, while maintaining a nearly constant initial energy density and temperature. However, this trend reaches its limit when b → 0. In this case, the initial system size is limited by the sizes of the participating nuclei. For symmetric PbPb collisions, this would be the size of a Pb nucleus. More energy and entropy can still be deposited into the fixed volume through fluctuations in the number of interacting partons. By examining the response of the temperature T to the increasing entropy density s at Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (11), the speed of sound can be extracted based on fundamental thermodynamic laws,

Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (12)

Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (13)

Here, in terms of experimental observables, s is directly proportional to Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (14), while the temperature T relates to the average transverse momentum Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (15) of emitted particles with respect to the beam axis [16]. Full hydrodynamic simulations, such as those made possible using the Trajectum model [19], have verified the above relationship, although there are features that are not captured, as will be discussed later. As the Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (16) value depends only on the relative variation in Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (17) and Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (18), any global changes to the observables, such as an increase in the system entropy through hadronic resonance decays [20], will not affect the result.

In this paper, we present a precise determination of the speed of sound in QGP using ultra-central PbPb collision data at Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (19), collected in 2018 by the CMS experiment at the CERN LHC. By achieving a level of precision of several percent, comparable to theoretical uncertainties, our results serve as a robust benchmark for comparison with hydrodynamic simulations and lattice QCD calculations of the EoS. These comparisons provide the most stringent and direct constraints on the degrees of freedom attained by the medium created in these collisions. Tabulated results are provided in the HEPData record for this analysis [21].

The CMS apparatus [22] is a multipurpose, nearly hermetic detector, designed to trigger on [23, 24] and identify electrons, muons, photons, and hadrons [2527]. The initial triggering is done with the level-1 system, which uses customized hardware to make the rapid online decision whether or not to accept an event and deliver it to the second system, the high level trigger (HLT). The HLT uses a large CPU farm to perform optimized online event reconstruction and characterize an event. A global 'particle-flow' algorithm [28] aims to reconstruct all individual particles in an event, combining information provided by the all-silicon pixel and strip tracker, and by the crystal electromagnetic and brass-scintillator hadron calorimeters, operating inside a 3.8 T superconducting solenoid, with data from the gas-ionization muon detectors embedded in the flux-return yoke outside the solenoid. Hadron forward (HF) calorimeters [29], made of steel and quartz fibers, extend the pseudorapidity (Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (20), where the polar angle θ is defined relative to the counterclockwise beam) coverage provided by the barrel and endcap detectors. Two zero-degree calorimeters (ZDCs) [30], made of quartz-fibers and plates embedded in tungsten absorbers, are used to detect neutrons from nuclear dissociation events.

The data analyzed, before applying the selection described below, consist of 4.27 Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (21) minimum bias events, corresponding to an integrated luminosity of 0.607 nb−1. The minimum bias events are triggered by requiring total energy signals above readout thresholds, which are in the range Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (22), on both sides of the HF calorimeters [24]. Beam-gas interactions and nonhadronic collisions are rejected by requiring the shapes of the clusters in the pixel tracker to be compatible with those expected from particles produced by a PbPb collision [31]. The events are also required to have at least one reconstructed primary vertex associated with two or more tracks within a distance of 15 cm from the nominal interaction point along the beam axis. The primary vertex is selected as the one with the highest track multiplicity in the event. Events with concurrent interactions per bunch crossing contribute to about 0.5% of the full data sample and are rejected based on the correlation of total energy deposited in the HF and ZDC detectors, following the procedure used in [32]. The collision centrality in PbPb events, i.e. the degree of overlap or impact parameter of the two colliding nuclei, is commonly determined by the total transverse energy deposit in both HF calorimeters, Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (23) [31]. As the main focus of this work is on collisions at small impact parameters, we analyzed only the 10% of PbPb events that had the largest Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (24). This class contains the ultra-central collision events of interest.

To ease the computational load for high-multiplicity central PbPb collisions, track reconstruction for PbPb events is done in two iterations. The first iteration reconstructs tracks from signals ('hits') in the silicon pixel and strip tracker that are compatible with trajectories of particles with Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (25), while the second iteration reconstructs tracks compatible with trajectories of particles with Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (26) using solely the pixel detector. In the analysis, the tracks have the additional selection requirement of Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (27) for the best tracking performance. More details on the track reconstruction and selection can be found in [33]. The tracking efficiency (εeff) and misreconstruction rate (εmis) are evaluated using the hydjet [34] event generator, together with a full Geant4 [35] simulation of the CMS detector response. These factors are combined to obtain an overall correction factor, Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (28), which is used to account for detector effects on the total number of reconstructed tracks. The εtrk factor is calibrated not only in terms of Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (29) and η, but also as a function of the detector occupancy. The occupancy is estimated by the total number of clusters registered in the silicon pixel tracker Npixel, where a weak linear decline of εtrk by up to 7% over an increase of Npixel by 30% is observed. In the analysis, each track is assigned a weight of Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (30) to account for track reconstruction effects.

The main experimental observable of this analysis is the mean transverse momentum Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (31) of charged particles in an event as a function of Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (32), where Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (33) and Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (34) are measured within the same η and Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (35) ranges (otherwise, rapidity-dependent entropy fluctuations would lead to a reduced signal [17]). Charged particle Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (36) spectra for Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (37) are measured for events in 50 GeV intervals of Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (38) from 3400 GeV to 5200 GeV, with tracking efficiency and misreconstruction effects corrected. To avoid any bias in estimating Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (39) and Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (40), it is necessary to extrapolate the measured Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (41) spectra to the full Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (42) range. The resulting Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (43) values (mean of the Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (44) spectra) from all Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (45) intervals are then plotted against the corresponding Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (46) values (integral of the Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (47) spectra) to form the final observable. The Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (48) variable essentially serves as a centrality estimator to vary the initial medium entropy density and temperature. In particular, as the Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (49) values are obtained in a forward η range that does not overlap with the range used to measure the corresponding Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (50) and Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (51) values, potential biases are avoided. For example, hard processes originating early in the collision tend to fragment into large numbers of high-Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (52) particles, yet these particles may not reflect an increase in the entropy and temperature of the QGP medium.

The extrapolation of the Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (53) spectra to the full Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (54) range is performed by fitting a Hagedorn function [36] to the measured Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (55) spectra over the range of Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (56) in each Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (57) interval. This method is found to provide an excellent description of the data [37] and models (Trajectum and hydjet). The chosen Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (58) range for the fitting is varied to the evaluate corresponding uncertainties. The fitted functions are then used to extrapolate the missing portions of the Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (59) spectra in the low-Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (60) region.

As the extraction of the speed of sound mainly depends on the relative variation of Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (61) with respect to Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (62) (see equation (1)), normalized quantities, Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (63) and Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (64), are used as the primary observables, where the Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (65) and Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (66) represent the mean transverse momentum and charged-particle multiplicity in a reference event class. Here, the centrality range chosen for the reference event class only needs to be close to that used for the speed of sound determination, and 5% most central events (as determined by Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (67) and denoted '0%–5%') is used. By normalizing both Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (68) and Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (69) by their values in the reference event class, most of the systematic uncertainties can be minimized. The Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (70) and Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (71) values obtained are found to be in good agreement with the ALICE results in the 0%–5% centrality range [37, 38]. Figure 2 shows the event fraction distribution as a function of the normalized multiplicity.

Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (72)

To extract the speed of sound, the expression that describes Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (79) as a function of Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (80) is taken from [17], as

Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (81)

where,

Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (82)

Here, Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (83) and σ represent the mean and root-mean-square width of the charged-particle multiplicity distribution at b = 0, normalized by Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (84). In figure 2, the Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (85) value corresponds to the vicinity of the location beyond which the knee-shaped distribution starts rapidly falling. For the region of Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (86), the Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (87) variable approximately reduces to Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (88), so equation (2) yields a value of unity. For the region of Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (89), the Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (90) variable saturates at Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (91) for sufficiently large Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (92). In this limit, equation (2) becomes a simple power function, with Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (93) being the power of the function. The parameters Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (94) and σ can be constrained by fitting the measured multiplicity distribution using the procedure described in [39]. The multiplicity distribution at fixed values of b is modeled using a Gaussian function. Integrating over b gives a minimum bias multiplicity distribution which can be fitted to data. As shown in figure 2, this fit provides a good description of the data. The results of this fit can be used to estimate the Gaussian mean and width at b = 0, yielding Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (95) and σ = 0.0272 with negligible uncertainties. Using the extracted Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (96) and σ values, a fit to the measured Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (97) as a function of Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (98) is performed using equation (2), thereby extracting the speed of sound. In practice, we limit the fit to the very high-multiplicity region of Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (99), as will be discussed in detail later.

The dominant sources of systematic uncertainties for the measured Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (100) and Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (101) values originate from the tracking correction and the extrapolation to the full Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (102) range. As mentioned earlier, using normalized quantities minimizes the majority of the systematic uncertainties. Systematic uncertainties are directly evaluated for the normalized quantities, as well as for Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (103) and Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (104). The tracking correction uncertainty is evaluated by varying the default track selections to a set of looser or tighter values. The maximum deviation with respect to the default results is taken as a systematic uncertainty, which is found to be Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (105) in Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (106) and Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (107) in the fitted Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (108) value. The Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (109) extrapolation uncertainty is estimated by varying the range of measured spectra fitted by the Hagedorn function to a lower limit of 0.3 or 0.5 GeV and an upper limit of 4 or 5 GeV. The resulting systematic uncertainty is found to be at most Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (110) for Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (111) and Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (112) for the Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (113) value. Systematic uncertainties for Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (114) associated with the choice of the lower fit limit in Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (115) are estimated by varying the limit from 1.13 to 1.17, resulting in an uncertainty of Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (116) in Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (117). Total uncertainties are obtained by adding the various sources in quadrature. Systematic uncertainties for Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (118) are extracted point-by-point as a function of Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (119).

The observed multiplicity dependence of the average transverse momentum, both normalized by their values in the 0%–5% centrality class, is presented in figure 3, within the kinematic range of Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (120) and extrapolated to the full Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (121) range in central PbPb events. Hydrodynamic simulations from the Trajectum [19, 40, 41] and Gardim et al [17] models are also shown for comparison. Both models use an EoS from lattice QCD calculations [42]. The Trajectum model is a computational framework to simulate the full evolution of heavy ion collisions, which includes the modeling of initial stages, a viscous hydrodynamic phase with transport coefficients, and a hadronic gas phase. Parameters of the Trajectum model are constrained by a global Bayesian analysis of a variety of experimental observables [19], where the band shown corresponds to uncertainties within the allowed range of Trajectum configuration parameters. The model of Gardim et al [17], besides the hydrodynamic phase, also considers the preequilibrium dynamics and hadronic interactions after thermal freeze-out. No uncertainties are evaluated for this model as only a single set of model parameters is used.

Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (122)

The Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (133) value first shows a very weak declining trend toward a local minimum around Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (134). At higher multiplicities, corresponding to ultra-central PbPb events, a steep rise is observed, which is consistent with the expected increase in temperature with entropy density, as schematically illustrated in figure 1. The observed trend, including the minimum around Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (135), is qualitatively consistent with the prediction by the Trajectum model. A slightly steeper rise at high multiplicities is observed for the Trajectum simulation when compared with the data. This suggests that the speed of sound used in the model may be slightly larger than is found in the QGP. However, this difference is not significant within experimental and theoretical uncertainties. The model by Gardim et al also predicts a rise of Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (136) at very high multiplicities, with a slope similar to that observed in the data. However, it shows a flat trend at lower multiplicities instead of the local minimum structure around Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (137) as seen in the data and the Trajectum model. The origin of the observed local minimum is not currently understood.

To directly extract the speed of sound, the multiplicity dependence of the Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (138) data in figure 3 is fitted by equation (2). Because the observed local minimum is not captured by the simplified model in equation (2), the fit is performed only in the high-multiplicity range with Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (139). The final result of the squared speed of sound is found to be Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (140) in natural units. The same fit is also performed to the prediction from the Trajectum model, resulting in Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (141), where the model uncertainty is again determined within the allowed parameter space constrained by a global Bayesian analysis [19].

To constrain the EoS, a simultaneous> determination of Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (142) and its corresponding temperature is necessary. Based on the hydrodynamic simulations discussed in [16, 17], the effective temperature (Teff) of the QGP phase is found to be given approximately by Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (143), with Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (144) quoted [16] based on a soft EoS. While the scaling factor relating Teff to Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (145) can depend on specific model assumptions, the theoretical uncertainty in this value is believed to be small compared to the quoted experimental uncertainties, thereby having no impact on the main conclusions drawn in this paper. In essence, Teff represents the initial temperature that a uniform fluid at rest would have if it possessed the same amount of energy and entropy as the QGP fluid does when it reaches its freeze-out state, the point at which the quarks become bound into hadrons. Due to longitudinal expansion and cooling, the Teff value is generally lower than the initial temperature of the QGP fluid. Nevertheless, it still characterizes a temperature in the QGP phase, to which the extracted Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (146) value based on the final-state Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (147) and Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (148) corresponds. Possible effects of shear and bulk viscosity are investigated in [16] and found to not impact this framework, as the shear viscosity increases Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (149) by about the same amount that the bulk viscosity decreases it. The Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (150) value is measured to be Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (151), leading to a Teff value for the ultra-central PbPb data of Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (152) (it varies by at most 2% toward the very end of Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (153) distribution within the 0%–5% centrality range). The statistical uncertainty is orders of magnitude smaller than the quoted systematic uncertainties.

Figure 4 depicts Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (154) as a function of Teff, with the CMS data point obtained from ultra-central PbPb collision data at Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (155). The results are compared to the Trajectum model, the Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (156) value extracted in [16], and lattice QCD predictions of the Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (157) value as a function of T [6]. The new CMS data allow for an unprecedented level of precision in the experimental determination of the speed of sound in an extended volume of QGP matter. The results exhibit excellent agreement with the lattice QCD prediction, with comparable uncertainties. Thus, our findings provide compelling and direct evidence for the formation of a deconfined QCD phase at LHC energies.

Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (158)

In summary, this study presents a measurement with a new hydrodynamic probe in ultrarelativistic nuclear collisions that results in the most precise determination to date of the speed of sound in an extended volume of QGP matter. By determining the dependence of the average transverse momentum on the total multiplicity for charged particles in nearly head-on PbPb collisions at a center-of-mass energy per nucleon pair of 5.02 TeV, a squared speed of sound of Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (164) in natural units is determined. The effective medium temperature, estimated using the mean transverse momentum, is Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (165). The excellent agreement of lattice QCDs predictions with the experimental results provides strong evidence for the existence of a deconfined phase of matter at extremely high temperatures.

We thank Fernando Gardim, Andre Veiga Giannini, Govert Nijs, Jean-Yves Ollitrault, and Wilke van der Schee for providing us with the model calculations used in figure 3.

We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid and other centers for delivering so effectively the computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construction and operation of the LHC, the CMS detector, and the supporting computing infrastructure provided by the following funding agencies: SC (Armenia), BMBWF and FWF (Austria); FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, FAPERGS, and FAPESP (Brazil); MES and BNSF (Bulgaria); CERN; CAS, MoST, and NSFC (China); MINCIENCIAS (Colombia); MSES and CSF (Croatia); RIF (Cyprus); SENESCYT (Ecuador); MoER, ERC PUT and ERDF (Estonia); Academy of Finland, MEC, and HIP (Finland); CEA and CNRS/IN2P3 (France); SRNSF (Georgia); BMBF, DFG, and HGF (Germany); GSRI (Greece); NKFIH (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland); INFN (Italy); MSIP and NRF (Republic of Korea); MES (Latvia); LAS (Lithuania); MOE and UM (Malaysia); BUAP, CINVESTAV, CONACYT, LNS, SEP, and UASLP-FAI (Mexico); MOS (Montenegro); MBIE (New Zealand); PAEC (Pakistan); MES and NSC (Poland); FCT (Portugal); MESTD (Serbia); MCIN/AEI and PCTI (Spain); MOSTR (Sri Lanka); Swiss Funding Agencies (Switzerland); MST (Taipei); MHESI and NSTDA (Thailand); TUBITAK and TENMAK (Turkey); NASU (Ukraine); STFC (United Kingdom); DOE and NSF (USA).

Individuals have received support from the Marie-Curie program and the European Research Council and Horizon 2020 Grant, Contract Nos. 675440, 724704, 752730, 758316, 765710, 824093, and COST Action CA16108 (European Union); the Leventis Foundation; the Alfred P. Sloan Foundation; the Alexander von Humboldt Foundation; the Science Committee, project no. 22rl-037 (Armenia); the Belgian Federal Science Policy Office; the Fonds pour la Formation à la Recherche dans l'Industrie et dans l'Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium); the F.R.S.-FNRS and FWO (Belgium) under the 'Excellence of Science—EOS' – be.h project n. 30820817; the Beijing Municipal Science & Technology Commission, No. Z191100007219010 and Fundamental Research Funds for the Central Universities (China); the Ministry of Education, Youth and Sports (MEYS) of the Czech Republic; the Shota Rustaveli National Science Foundation, grant FR-22-985 (Georgia); the Deutsche Forschungsgemeinschaft (DFG), under Germany's Excellence Strategy—EXC 2121 'Quantum Universe'—390833306, and under Project Number 400140256—GRK2497; the Hellenic Foundation for Research and Innovation (HFRI), Project Number 2288 (Greece); the Hungarian Academy of Sciences, the New National Excellence Program—ÚNKP, the NKFIH research grants K 124845, K 124850, K 128713, K 128786, K 129058, K 131991, K 133046, K 138136, K 143460, K 143477, 2020-2.2.1-ED-2021-00181, and TKP2021-NKTA-64 (Hungary); the Council of Science and Industrial Research, India; ICSC—National Research Center for High Performance Computing, Big Data and Quantum Computing, funded by the Next GenerationEU program (Italy); the Latvian Council of Science; the Ministry of Education and Science, Project No. 2022/WK/14, and the National Science Center, Contracts Opus 2021/41/B/ST2/01369 and 2021/43/B/ST2/01552 (Poland); the Fundação para a Ciência e a Tecnologia, grant CEECIND/01334/2018 (Portugal); the National Priorities Research Program by Qatar National Research Fund; MCIN/AEI/10.13039/501100011033, ERDF 'a way of making Europe', and the Programa Estatal de Fomento de la Investigación Científica y Técnica de Excelencia María de Maeztu, Grant MDM-2017-0765 and Programa Severo Ochoa del Principado de Asturias (Spain); the Chulalongkorn Academic into Its 2nd Century Project Advancement Project, and the National Science, Research and Innovation Fund via the Program Management Unit for Human Resources & Institutional Development, Research and Innovation, Grant B37G660013 (Thailand); the Kavli Foundation; the Nvidia Corporation; the SuperMicro Corporation; the Welch Foundation, contract C-1845; and the Weston Havens Foundation (USA).

Release and preservation of data used by the CMS Collaboration as the basis for publications is guided by the CMS policy as stated in CMS data preservation, re-use and open access policy.

A Hayrapetyan, A Tumasyan1

Yerevan Physics Institute, Yerevan, Armenia

W Adam, J W Andrejkovic, T Bergauer, S Chatterjee, K Damanakis, M Dragicevic, P S Hussain, M Jeitler2, N Krammer, A Li, D Liko, I Mikulec, J Schieck2, R Schöfbeck, D Schwarz, M Sonawane, S Templ, W Waltenberger, C -E Wulz2

Institut für Hochenergiephysik, Vienna, Austria

M R Darwish3, T Janssen, P Van Mechelen

Universiteit Antwerpen, Antwerpen, Belgium

E S Bols, J D'Hondt, S Dansana, A De Moor, M Delcourt, H El Faham, S Lowette, I Makarenko, D Müller, A.R Sahasransu, S Tavernier, M Tytgat4, G.P Van Onsem, S Van Putte, D Vannerom

Vrije Universiteit Brussel, Brussel, Belgium

B Clerbaux, A K Das, G De Lentdecker, L Favart, P Gianneios, D Hohov, J Jaramillo, A Khalilzadeh, K Lee, M Mahdavikhorrami, A Malara, S Paredes, N Postiau, L Thomas, M Vanden Bemden, C Vander Velde, P Vanlaer

Université Libre de Bruxelles, Bruxelles, Belgium

M De Coen, D Dobur, Y Hong, J Knolle, L Lambrecht, G Mestdach, K Mota Amarilo, C Rendón, A Samalan, K Skovpen, N Van Den Bossche, J van der Linden, L Wezenbeek

Ghent University, Ghent, Belgium

A Benecke, A Bethani, G Bruno, C Caputo, C Delaere, I S Donertas, A Giammanco, K Jaffel, Sa Jain, V Lemaitre, J Lidrych, P Mastrapasqua, K Mondal, T T Tran, S Wertz

Université Catholique de Louvain, Louvain-la-Neuve, Belgium

G A Alves, E Coelho, C Hensel, T Menezes De Oliveira, A Moraes, P Rebello Teles, M Soeiro

Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil

W L Aldá Júnior, M Alves Gallo Pereira, M Barroso Ferreira Filho, H Brandao Malbouisson, W Carvalho, J Chinellato5, E M Da Costa, G G Da Silveira6, D De Jesus Damiao, S Fonseca De Souza, R Gomes De Souza, J Martins7, C Mora Herrera, L Mundim, H Nogima, J P Pinheiro, A Santoro, A Sznajder, M Thiel, A Vilela Pereira

Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil

C A Bernardes6, L Calligaris, T R Fernandez Perez Tomei, E M Gregores, P G Mercadante, S F Novaes, B Orzari, Sandra S Padula

Universidade Estadual Paulista, Universidade Federal do ABC, São Paulo, Brazil

A Aleksandrov, G Antchev, R Hadjiiska, P Iaydjiev, M Misheva, M Shopova, G Sultanov

Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria

A Dimitrov, L Litov, B Pavlov, P Petkov, A Petrov, E Shumka

University of Sofia, Sofia, Bulgaria

S Keshri, S Thakur

Instituto De Alta Investigación, Universidad de Tarapacá, Casilla 7 D, Arica, Chile

T Cheng, T Javaid, L Yuan

Beihang University, Beijing, People's Republic of China

Z Hu, J Liu, K Yi8,9

Department of Physics, Tsinghua University, Beijing, People's Republic of China

G.M Chen10, H S Chen10, M Chen10, F Iemmi, C H Jiang, A Kapoor11, H Liao, Z -A Liu12, R Sharma13, J N Song12, J Tao, C Wang10, J Wang, Z Wang10, H Zhang

Institute of High Energy Physics, Beijing, People's Republic of China

A Agapitos, Y Ban, A Levin, C Li, Q Li, Y Mao, S J Qian, X Sun, D Wang, H Yang, L Zhang, C Zhou

State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing, People's Republic of China

Z You

Sun Yat-Sen University, Guangzhou, People's Republic of China

N Lu

University of Science and Technology of People's Republic of China , Hefei, People's Republic of China

G Bauer14

Nanjing Normal University, Nanjing, People's Republic of China

X Gao15, D Leggat, H Okawa

Institute of Modern Physics and Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) - Fudan University, Shanghai, People's Republic of China

Z Lin, C Lu, M Xiao

Zhejiang University, Hangzhou, Zhejiang, People's Republic of China

C Avila, D A Barbosa Trujillo, A Cabrera, C Florez, J Fraga, J A Reyes Vega

Universidad de Los Andes, Bogota, Colombia

J Mejia Guisao, F Ramirez, M Rodriguez, J D Ruiz Alvarez

Universidad de Antioquia, Medellin, Colombia

D Giljanovic, N Godinovic, D Lelas, A Sculac

University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, Split, Croatia

M Kovac, T Sculac

University of Split, Faculty of Science, Split, Croatia

P Bargassa, V Brigljevic, B K Chitroda, D Ferencek, S Mishra, A Starodumov16, T Susa

Institute Rudjer Boskovic, Zagreb, Croatia

A Attikis, K Christoforou, S Konstantinou, J Mousa, C Nicolaou, F Ptochos, P A Razis, H Rykaczewski, H Saka, A Stepennov

University of Cyprus, Nicosia, Cyprus

M Finger, M Finger Jr, A Kveton

Charles University, Prague, Czech Republic

E Ayala

Escuela Politecnica Nacional, Quito, Ecuador

E Carrera Jarrin

Universidad San Francisco de Quito, Quito, Ecuador

A A Abdelalim17,18, E Salama19,20

Academy of Scientific Research and Technology of the Arab Republic of Egypt, Egyptian Network of High Energy Physics, Cairo, Egypt

A Lotfy, M A Mahmoud

Center for High Energy Physics (CHEP-FU), Fayoum University, El-Fayoum, Egypt

K Ehataht, M Kadastik, T Lange, S Nandan, C Nielsen, J Pata, M Raidal, L Tani, C Veelken

National Institute of Chemical Physics and Biophysics, Tallinn, Estonia

H Kirschenmann, K Osterberg, M Voutilainen

Department of Physics, University of Helsinki, Helsinki, Finland

S Bharthuar, E Brücken, F Garcia, K T S Kallonen, R Kinnunen, T Lampén, K Lassila-Perini, S Lehti, T Lindén, L Martikainen, M Myllymäki, M m Rantanen, H Siikonen, E Tuominen, J Tuominiemi

Helsinki Institute of Physics, Helsinki, Finland

P Luukka, H Petrow

Lappeenranta-Lahti University of Technology, Lappeenranta, Finland

M Besancon, F Couderc, M Dejardin, D Denegri, J L Faure, F Ferri, S Ganjour, P Gras, G Hamel de Monchenault, V Lohezic, J Malcles, J Rander, A Rosowsky, M.Ö Sahin, A Savoy-Navarro21, P Simkina, M Titov, M Tornago

IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France

C Baldenegro Barrera, F Beaudette, A Buchot Perraguin, P Busson, A Cappati, C Charlot, M Chiusi, F Damas, O Davignon, A De Wit, B A Fontana Santos Alves, S Ghosh, A Gilbert, R Granier de Cassagnac, A Hakimi, B Harikrishnan, L Kalipoliti, G Liu, J Motta, M Nguyen, C Ochando, L Portales, R Salerno, J B Sauvan, Y Sirois, A Tarabini, E Vernazza, A Zabi, A Zghiche

Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau, France

J -L Agram22, J Andrea, D Apparu, D Bloch, J -M Brom, E.C Chabert, C Collard, S Falke, U Goerlach, C Grimault, R Haeberle, A -C Le Bihan, M Meena, G Saha, M A Sessini, P Van Hove

Université de Strasbourg, CNRS, IPHC UMR 7178, Strasbourg, France

S Beauceron, B Blancon, G Boudoul, N Chanon, J Choi, D Contardo, P Depasse, C Dozen23, H El Mamouni, J Fay, S Gascon, M Gouzevitch, C Greenberg, G Grenier, B Ille, I B Laktineh, M Lethuillier, L Mirabito, S Perries, A Purohit, M Vander Donckt, P Verdier, J Xiao

Institut de Physique des 2 Infinis de Lyon (IP2I ), Villeurbanne, France

D Chokheli, I Lomidze, Z Tsamalaidze16

Georgian Technical University, Tbilisi, Georgia

V Botta, L Feld, K Klein, M Lipinski, D Meuser, A Pauls, N Röwert, M Teroerde

RWTH Aachen University, I. Physikalisches Institut, Aachen, Germany

S Diekmann, A Dodonova, N Eich, D Eliseev, F Engelke, J Erdmann, M Erdmann, P Fackeldey, B Fischer, T Hebbeker, K Hoepfner, F Ivone, A Jung, M y Lee, L Mastrolorenzo, F Mausolf, M Merschmeyer, A Meyer, S Mukherjee, D Noll, F Nowotny, A Pozdnyakov, Y Rath, W Redjeb, F Rehm, H Reithler, U Sarkar, V Sarkisovi, A Schmidt, A Sharma, J L Spah, A Stein, F Torres Da Silva De Araujo24, L Vigilante, S Wiedenbeck, S Zaleski

RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany

C Dziwok, G Flügge, W Haj Ahmad25, T Kress, A Nowack, O Pooth, A Stahl, T Ziemons, A Zotz

RWTH Aachen University, III. Physikalisches Institut B, Aachen, Germany

H Aarup Petersen, M Aldaya Martin, J Alimena, S Amoroso, Y An, S Baxter, M Bayatmakou, H Becerril Gonzalez, O Behnke, A Belvedere, S Bhattacharya, F Blekman26, K Borras27, A Campbell, A Cardini, C Cheng, F Colombina, S Consuegra Rodríguez, G Correia Silva, M De Silva, G Eckerlin, D Eckstein, L I Estevez Banos, O Filatov, E Gallo26, A Geiser, A Giraldi, G Greau, V Guglielmi, M Guthoff, A Hinzmann, A Jafari28, L Jeppe, N Z Jomhari, B Kaech, M Kasemann, C Kleinwort, R Kogler, M Komm, D Krücker, W Lange, D Leyva Pernia, K Lipka29, W Lohmann30, R Mankel, I -A Melzer-Pellmann, M Mendizabal Morentin, A B Meyer, G Milella, A Mussgiller, L P Nair, A Nürnberg, Y Otarid, J Park, D Pérez Adán, E Ranken, A Raspereza, B Ribeiro Lopes, J Rübenach, A Saggio, M Scham31,27, S Schnake27, P Schütze, C Schwanenberger26, D Selivanova, K Sharko, M Shchedrolosiev, R E Sosa Ricardo, D Stafford, F Vazzoler, A Ventura Barroso, R Walsh, Q Wang, Y Wen, K Wichmann, L Wiens27, C Wissing, Y Yang, A Zimermmane Castro Santos

Deutsches Elektronen-Synchrotron, Hamburg, Germany

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University of Hamburg, Hamburg, Germany

S Brommer, M Burkart, E Butz, T Chwalek, A Dierlamm, A Droll, N Faltermann, M Giffels, A Gottmann, F Hartmann32, R Hofsaess, M Horzela, U Husemann, J Kieseler, M Klute, R Koppenhöfer, J M Lawhorn, M Link, A Lintuluoto, S Maier, S Mitra, M Mormile, Th Müller, M Neukum, M Oh, M Presilla, G Quast, K Rabbertz, B Regnery, N Shadskiy, I Shvetsov, H J Simonis, M Toms, N Trevisani, R Ulrich, R.F Von Cube, M Wassmer, S Wieland, F Wittig, R Wolf, X Zuo

Karlsruher Institut fuer Technologie, Karlsruhe, Germany

G Anagnostou, G Daskalakis, A Kyriakis, A Papadopoulos32, A Stakia

Institute of Nuclear and Particle Physics (INPP), NCSR Demokritos, Aghia Paraskevi, Greece

P Kontaxakis, G Melachroinos, A Panagiotou, I Papavergou, I Paraskevas, N Saoulidou, K Theofilatos, E Tziaferi, K Vellidis, I Zisopoulos

National and Kapodistrian University of Athens, Athens, Greece

G Bakas, T Chatzistavrou, G Karapostoli, K Kousouris, I Papakrivopoulos, E Siamarkou, G Tsipolitis, A Zacharopoulou

National Technical University of Athens, Athens, Greece

K Adamidis, I Bestintzanos, I Evangelou, C Foudas, C Kamtsikis, P Katsoulis, P Kokkas, P G Kosmoglou Kioseoglou, N Manthos, I Papadopoulos, J Strologas

University of Ioánnina, Ioánnina, Greece

M Bartók33, C Hajdu, D Horvath34,35, K Márton, F Sikler, V Veszpremi

HUN-REN Wigner Research Centre for Physics, Budapest, Hungary

M Csanád, K Farkas, M M A Gadallah36, Á Kadlecsik, P Major, K Mandal, G Pásztor, A.J Rádl37, G.I Veres

MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös Loránd University, Budapest, Hungary

P Raics, B Ujvari, G Zilizi

Faculty of Informatics, University of Debrecen, Debrecen, Hungary

G Bencze, S Czellar, J Molnar, Z Szillasi

Institute of Nuclear Research ATOMKI, Debrecen, Hungary

T Csorgo37, F Nemes37, T Novak

Karoly Robert Campus, MATE Institute of Technology, Gyongyos, Hungary

J Babbar, S Bansal, S.B Beri, V Bhatnagar, G Chaudhary, S Chauhan, N Dhingra38, A Kaur, A Kaur, H Kaur, M Kaur, S Kumar, K Sandeep, T Sheokand, J B Singh, A Singla

Panjab University, Chandigarh, India

A Ahmed, A Bhardwaj, A Chhetri, B C Choudhary, A Kumar, A Kumar, M Naimuddin, K Ranjan, S Saumya

University of Delhi, Delhi, India

S Baradia, S Barman39, S Bhattacharya, S Dutta, S Dutta, S Sarkar

Saha Institute of Nuclear Physics, HBNI, Kolkata, India

M M Ameen, P K Behera, S C Behera, S Chatterjee, P Jana, P Kalbhor, J R Komaragiri40, D Kumar40, L Panwar40, P R Pujahari, N R Saha, A Sharma, A K Sikdar, S Verma

Indian Institute of Technology Madras, Madras, India

S Dugad, M Kumar, G B Mohanty, P Suryadevara

Tata Institute of Fundamental Research-A, Mumbai, India

A Bala, S Banerjee, R M Chatterjee, R K Dewanjee41, M Guchait, Sh Jain, A Jaiswal, S Karmakar, S Kumar, G Majumder, K Mazumdar, S Parolia, A Thachayath

Tata Institute of Fundamental Research-B, Mumbai, India

S Bahinipati42, C Kar, D Maity43, P Mal, T Mishra, V K Muraleedharan Nair Bindhu43, K Naskar43, A Nayak43, P Sadangi, P Saha, S K Swain, S Varghese43, D Vats43

National Institute of Science Education and Research, An OCC of Homi Bhabha National Institute, Bhubaneswar, Odisha, India

S Acharya44, A Alpana, S Dube, B Gomber44, B Kansal, A Laha, B Sahu44, S Sharma, K Y Vaish

Indian Institute of Science Education and Research (IISER), Pune, India

H Bakhshiansohi45, E Khazaie46, M Zeinali47

Isfahan University of Technology, Isfahan, Iran

S Chenarani48, S M Etesami, M Khakzad, M Mohammadi Najafabadi

Institute for Research in Fundamental Sciences (IPM), Tehran, Iran

M Grunewald

University College Dublin, Dublin, Ireland

M Abbresciaa,b, R Alya,c,17, A Colaleoa,b, D Creanzaa,c, B D'Anzia,b, N De Filippisa,c, M De Palmaa,b, A Di Florioa,c, W Elmetenaweea,b,17, L Fiorea, G Iasellia,c, M Loukaa,b, G Maggia,c, M Maggia, I Margjekaa,b, V Mastrapasquaa,b, S Mya,b, S Nuzzoa,b, A Pellecchiaa,b, A Pompilia,b, G Pugliesea,c, R Radognaa, G Ramirez-Sancheza,c, D Ramosa, A Ranieria, L Silvestrisa, F M Simonea,b, Ü Sözbilira, A Stamerraa, R Vendittia, P Verwilligena, A Zazaa,b

INFN Sezione di Baria, Università di Barib, Politecnico di Baric, Bari, Italy

G Abbiendia, C Battilanaa,b, D Bonacorsia,b, L Borgonovia, R Campaninia,b, P Capiluppia,b, A Castroa,b, F R Cavalloa, M Cuffiania,b, T Diotalevia,b, F Fabbria, A Fanfania,b, D Fasanellaa,b, P Giacomellia, L Giommia,b, C Grandia, L Guiduccia,b, S Lo Meoa,49, L Lunertia,b, S Marcellinia, G Masettia, F L Navarriaa,b, A Perrottaa, F Primaveraa,b, A M Rossia,b, T Rovellia,b, G P Sirolia,b

INFN Sezione di Bolognaa, Università di Bolognab, Bologna, Italy

S Costaa,b,50, A Di Mattiaa, R Potenzaa,b, A Tricomia,b,50, C Tuvea,b

INFN Sezione di Cataniaa, Università di Cataniab, Catania, Italy

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INFN Sezione di Firenzea, Università di Firenzeb, Firenze, Italy

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INFN Laboratori Nazionali di Frascati, Frascati, Italy

P Chatagnona, F Ferroa, E Robuttia, S Tosia,b

INFN Sezione di Genovaa, Università di Genovab, Genova, Italy

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INFN Sezione di Milano-Bicoccaa, Università di Milano-Bicoccab, Milano, Italy

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INFN Sezione di Napolia, Università di Napoli 'Federico II'b, Napoli, Italy; Università della Basilicatac, Potenza, Italy; Scuola Superiore Meridionale (SSM)d, Napoli, Italy

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INFN Sezione di Padovaa, Università di Padovab, Padova, Italy; Università di Trentoc, Trento, Italy

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INFN Sezione di Paviaa, Università di Paviab, Pavia, Italy

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INFN Sezione di Perugiaa, Università di Perugiab, Perugia, Italy

P Asenova,b, P Azzurria, G Bagliesia, R Bhattacharyaa, L Bianchinia,b, T Boccalia, E Bossinia, D Bruschinia,c, R Castaldia, M A Cioccia,b, M Cipriania,b, V D'Amantea,d, R Dell'Orsoa, S Donatoa, A Giassia, F Ligabuea,c, D Matos Figueiredoa, A Messineoa,b, M Musicha,b, F Pallaa, A Rizzia,b, G Rolandia,c, S Roy Chowdhurya, T Sarkara, A Scribanoa, P Spagnoloa, R Tenchinia, G Tonellia,b, N Turinia,d, A Venturia, P G Verdinia

INFN Sezione di Pisaa, Università di Pisab, Scuola Normale Superiore di Pisac, Pisa, Italy; Università di Sienad, Siena, Italy

P Barriaa, M Campanaa,b, F Cavallaria, L Cunqueiro Mendeza,b, D Del Rea,b, E Di Marcoa, M Diemoza, F Erricoa,b, E Longoa,b, P Meridiania, J Mijuskovica,b, G Organtinia,b, F Pandolfia, R Paramattia,b, C Quarantaa,b, S Rahatloua,b, C Rovellia, F Santanastasioa,b, L Soffia

INFN Sezione di Romaa, Sapienza Università di Romab, Roma, Italy

N Amapanea,b, R Arcidiaconoa,c, S Argiroa,b, M Arneodoa,c, N Bartosika, R Bellana,b, A Belloraa,b, C Biinoa, C Borcaa,b, N Cartigliaa, M Costaa,b, R Covarellia,b, N Demariaa, L Fincoa, M Grippoa,b, B Kiania,b, F Leggera, F Luongoa,b, C Mariottia, L Markovica,b, S Masellia, A Meccaa,b, E Migliorea,b, M Montenoa, R Mulargiaa, M M Obertinoa,b, G Ortonaa, L Pachera,b, N Pastronea, M Pelliccionia, M Ruspaa,c, F Sivieroa,b, V Solaa,b, A Solanoa,b, A Staianoa, C Tarriconea,b, D Trocinoa, G Umoreta,b, E Vlasova,b

INFN Sezione di Torinoa, Università di Torinob, Torino, Italy; Università del Piemonte Orientalec, Novara, Italy

S Belfortea, V Candelisea,b, M Casarsaa, F Cossuttia, K De Leoa,b, G Della Riccaa,b

INFN Sezione di Triestea, Università di Triesteb, Trieste, Italy

S Dogra, J Hong, C Huh, B Kim, D.H Kim, J Kim, H Lee, S.W Lee, C.S Moon, Y.D Oh, M.S Ryu, S Sekmen, Y.C Yang

Kyungpook National University, Daegu, Republic of Korea

M S Kim

Department of Mathematics and Physics - GWNU, Gangneung, Republic of Korea

G Bak, P Gwak, H Kim, D H Moon

Chonnam National University, Institute for Universe and Elementary Particles, Kwangju, Republic of Korea

E Asilar, D Kim, T J Kim, J A Merlin

Hanyang University, Seoul, Republic of Korea

S Choi, S Han, B Hong, K Lee, K S Lee, S Lee, J Park, S K Park, J Yoo

Republic of Korea University, Seoul, Republic of Korea

J Goh, S Yang

Kyung Hee University, Department of Physics, Seoul, Republic of Korea

H S Kim, Y Kim, S Lee

Sejong University, Seoul, Republic of Korea

J Almond, J H Bhyun, J Choi, W Jun, J Kim, S Ko, H Kwon, H Lee, J Lee, J Lee, B H Oh, S B Oh, H Seo, U K Yang, I Yoon

Seoul National University, Seoul, Republic of Korea

W Jang, D Y Kang, Y Kang, S Kim, B Ko, J S H Lee, Y Lee, I C Park, Y Roh, I.J Watson

University of Seoul, Seoul, Republic of Korea

S Ha, H D Yoo

Yonsei University, Department of Physics, Seoul, Republic of Korea

M Choi, M R Kim, H Lee, Y Lee, I Yu

Sungkyunkwan University, Suwon, Republic of Korea

T Beyrouthy, Y Maghrbi

College of Engineering and Technology, American University of the Middle East (AUM), Dasman, Kuwait

K Dreimanis, A Gaile, G Pikurs, A Potrebko, M Seidel, V Veckalns55

Riga Technical University, Riga, Latvia

N R Strautnieks

University of Latvia (LU), Riga, Latvia

M Ambrozas, A Juodagalvis, A Rinkevicius, G Tamulaitis

Vilnius University, Vilnius, Lithuania

N Bin Norjoharuddeen, I Yusuff56, Z Zolkapli

National Centre for Particle Physics, Universiti Malaya, Kuala Lumpur, Malaysia

J F Benitez, A Castaneda Hernandez, H A Encinas Acosta, L G Gallegos Maríñez, M León Coello, J A Murillo Quijada, A Sehrawat, L Valencia Palomo

Universidad de Sonora (UNISON), Hermosillo, Mexico

G Ayala, H Castilla-Valdez, H Crotte Ledesma, E De La Cruz-Burelo, I Heredia-De La Cruz57, R Lopez-Fernandez, C A Mondragon Herrera, A Sánchez Hernández

Centro de Investigacion y de Estudios Avanzados del IPN, Mexico City, Mexico

C Oropeza Barrera, M Ramírez García

Universidad Iberoamericana, Mexico City, Mexico

I Bautista, I Pedraza, H A Salazar Ibarguen, C Uribe Estrada

Benemerita Universidad Autonoma de Puebla, Puebla, Mexico

I Bubanja, N Raicevic

University of Montenegro, Podgorica, Montenegro

P H Butler

University of Canterbury, Christchurch, New Zealand

A Ahmad, M I Asghar, A Awais, M I M Awan, H R Hoorani, W A Khan

National Centre for Physics, Quaid-I-Azam University, Islamabad, Pakistan

V Avati, L Grzanka, M Malawski

AGH University of Krakow, Faculty of Computer Science, Electronics and Telecommunications, Krakow, Poland

H Bialkowska, M Bluj, B Boimska, M Górski, M Kazana, M Szleper, P Zalewski

National Centre for Nuclear Research, Swierk, Poland

K Bunkowski, K Doroba, A Kalinowski, M Konecki, J Krolikowski, A Muhammad

Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Warsaw, Poland

K Pozniak, W Zabolotny

Warsaw University of Technology, Warsaw, Poland

M Araujo, D Bastos, C Beirão Da Cruz E Silva, A Boletti, M Bozzo, T Camporesi, G Da Molin, P Faccioli, M Gallinaro, J Hollar, N Leonardo, T Niknejad, A Petrilli, M Pisano, J Seixas, J Varela, J W Wulff

Laboratório de Instrumentação e Física Experimental de Partículas, Lisboa, Portugal

P Adzic, P Milenovic

Faculty of Physics, University of Belgrade, Belgrade, Serbia

M Dordevic, J Milosevic, V Rekovic

VINCA Institute of Nuclear Sciences, University of Belgrade, Belgrade, Serbia

M Aguilar-Benitez, J Alcaraz Maestre, Cristina F Bedoya, M Cepeda, M Cerrada, N Colino, B De La Cruz, A Delgado Peris, A Escalante Del Valle, D Fernández Del Val, J P Fernández Ramos, J Flix, M C Fouz, O Gonzalez Lopez, S Goy Lopez, J M Hernandez, M I Josa, D Moran, C M Morcillo Perez, Á Navarro Tobar, C Perez Dengra, A Pérez-Calero Yzquierdo, J Puerta Pelayo, I Redondo, D D Redondo Ferrero, L Romero, S Sánchez Navas, L Urda Gómez, J Vazquez Escobar, C Willmott

Centro de Investigaciones Energéticas Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain

J F de Trocóniz

Universidad Autónoma de Madrid, Madrid, Spain

B Alvarez Gonzalez, J Cuevas, J Fernandez Menendez, S Folgueras, I Gonzalez Caballero, J R González Fernández, E Palencia Cortezon, C Ramón Álvarez, V Rodríguez Bouza, A Soto Rodríguez, A Trapote, C Vico Villalba, P Vischia

Universidad de Oviedo, Instituto Universitario de Ciencias y Tecnologías Espaciales de Asturias (ICTEA), Oviedo, Spain

S Bhowmik, S Blanco Fernández, J A Brochero Cifuentes, I J Cabrillo, A Calderon, J Duarte Campderros, M Fernandez, G Gomez, C Lasaosa García, C Martinez Rivero, P Martinez Ruiz del Arbol, F Matorras, P Matorras Cuevas, E Navarrete Ramos, J Piedra Gomez, L Scodellaro, I Vila, J M Vizan Garcia

Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria, Santander, Spain

M K Jayananda, B Kailasapathy58, D U J Sonnadara, D D C Wickramarathna

University of Colombo, Colombo, Sri Lanka

W G D Dharmaratna59, K Liyanage, N Perera, N Wickramage

University of Ruhuna, Department of Physics, Matara, Sri Lanka

D Abbaneo, C Amendola, E Auffray, G Auzinger, J Baechler, D Barney, A Bermúdez Martínez, M Bianco, B Bilin, A A Bin Anuar, A Bocci, C Botta, E Brondolin, C Caillol, G Cerminara, N Chernyavskaya, D d'Enterria, A Dabrowski, A David, A De Roeck, M M Defranchis, M Deile, M Dobson, L Forthomme, G Franzoni, W Funk, S Giani, D Gigi, K Gill, F Glege, L Gouskos, M Haranko, J Hegeman, B Huber, V Innocente, T James, P Janot, S Laurila, P Lecoq, E Leutgeb, C Lourenço, B Maier, L Malgeri, M Mannelli, A C Marini, M Matthewman, F Meijers, S Mersi, E Meschi, V Milosevic, F Monti, F Moortgat, M Mulders, I Neutelings, S Orfanelli, F Pantaleo, G Petrucciani, A Pfeiffer, M Pierini, D Piparo, H Qu, D Rabady, G Reales Gutiérrez, M Rovere, H Sakulin, S Scarfi, C Schwick, M Selvaggi, A Sharma, K Shchelina, P Silva, P Sphicas60, A G Stahl Leiton, A Steen, S Summers, D Treille, P Tropea, A Tsirou, D Walter, J Wanczyk61, J Wang, S Wuchterl, P Zehetner, P Zejdl, W D Zeuner

CERN, European Organization for Nuclear Research, Geneva, Switzerland

T Bevilacqua62, L Caminada62, A Ebrahimi, W Erdmann, R Horisberger, Q Ingram, H C Kaestli, D Kotlinski, C Lange, M Missiroli62, L Noehte62, T Rohe

Paul Scherrer Institut, Villigen, Switzerland

T K Aarrestad, K Androsov61, M Backhaus, A Calandri, C Cazzaniga, K Datta, A De Cosa, G Dissertori, M Dittmar, M Donegà, F Eble, M Galli, K Gedia, F Glessgen, C Grab, D Hits, W Lustermann, A -M Lyon, R A Manzoni, M Marchegiani, L Marchese, C Martin Perez, A Mascellani61, F Nessi-Tedaldi, F Pauss, V Perovic, S Pigazzini, C Reissel, T Reitenspiess, B Ristic, F Riti, D Ruini, R Seidita, J Steggemann61, D Valsecchi, R Wallny

ETH Zurich - Institute for Particle Physics and Astrophysics (IPA), Zurich, Switzerland

C Amsler63, P Bärtschi, D Brzhechko, M.F Canelli, K Cormier, J K Heikkilä, M Huwiler, W Jin, A Jofrehei, B Kilminster, S Leontsinis, S P Liechti, A Macchiolo, P Meiring, U Molinatti, A Reimers, P Robmann, S Sanchez Cruz, M Senger, Y Takahashi, R Tramontano

Universität Zürich, Zurich, Switzerland

C Adloff64, D Bhowmik, C M Kuo, W Lin, P K Rout, P C Tiwari40, S S Yu

National Central University, Chung-Li, Taiwan

L Ceard, Y Chao, K F Chen, P s Chen, Z g Chen, A De Iorio, W -S Hou, T h Hsu, Y w Kao, R Khurana, G Kole, Y y Li, R -S Lu, E Paganis, X f Su, J Thomas-Wilsker, L s Tsai, H y Wu, E Yazgan

National Taiwan University (NTU), Taipei, Taiwan

C Asawatangtrakuldee, N Srimanobhas, V Wachirapusitanand

High Energy Physics Research Unit, Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok, Thailand

D Agyel, F Boran, Z S Demiroglu, F Dolek, I Dumanoglu65, E Eskut, Y Guler66, E Gurpinar Guler66, C Isik, O Kara, A Kayis Topaksu, U Kiminsu, G Onengut, K Ozdemir67, A Polatoz, B Tali68, U G Tok, S Turkcapar, E Uslan, I S Zorbakir

Çukurova University, Physics Department, Science and Art Faculty, Adana, Turkey

M Yalvac69

Middle East Technical University, Physics Department, Ankara, Turkey

B Akgun, I O Atakisi, E Gülmez, M Kaya70, O Kaya71, S Tekten72

Bogazici University, Istanbul, Turkey

A Cakir, K Cankocak65,73, Y Komurcu, S Sen74

Istanbul Technical University, Istanbul, Turkey

O Aydilek, S Cerci68, V Epshteyn, B Hacisahinoglu, I Hos75, B Kaynak, S Ozkorucuklu, O Potok, H Sert, C Simsek, C Zorbilmez

Istanbul University, Istanbul, Turkey

B Isildak76, D Sunar Cerci68

Yildiz Technical University, Istanbul, Turkey

A Boyaryntsev, B Grynyov

Institute for Scintillation Materials of National Academy of Science of Ukraine, Kharkiv, Ukraine

L Levchuk

National Science Centre, Kharkiv Institute of Physics and Technology, Kharkiv, Ukraine

D Anthony, J J Brooke, A Bundock, F Bury, E Clement, D Cussans, H Flacher, M Glowacki, J Goldstein, H F Heath, L Kreczko, S Paramesvaran, L Robertshaw, S Seif El Nasr-Storey, V J Smith, N Stylianou77, K Walkingshaw Pass, R White

University of Bristol, Bristol, United Kingdom

A H Ball, K W Bell, A Belyaev78, C Brew, R M Brown, D J A Cockerill, C Cooke, K V Ellis, K Harder, S Harper, M -L Holmberg79, J Linacre, K Manolopoulos, D M Newbold, E Olaiya, D Petyt, T Reis, G Salvi, T Schuh, C H Shepherd-Themistocleous, I R Tomalin, T Williams

Rutherford Appleton Laboratory, Didcot, United Kingdom

R Bainbridge, P Bloch, C E Brown, O Buchmuller, V Cacchio, C A Carrillo Montoya, G S Chahal80, D Colling, J S Dancu, I Das, P Dauncey, G Davies, J Davies, M Della Negra, S Fayer, G Fedi, G Hall, M H Hassanshahi, A Howard, G Iles, M Knight, J Langford, J León Holgado, L Lyons, A -M Magnan, S Malik, M Mieskolainen, J Nash81, M Pesaresi, B C Radburn-Smith, A Richards, A Rose, K Savva, C Seez, R Shukla, A Tapper, K Uchida, G P Uttley, L H Vage, T Virdee32, M Vojinovic, N Wardle, D Winterbottom

Imperial College, London, United Kingdom

K Coldham, J E Cole, A Khan, P Kyberd, I D Reid

Brunel University, Uxbridge, United Kingdom

S Abdullin, A Brinkerhoff, B Caraway, J Dittmann, K Hatakeyama, J Hiltbrand, B McMaster, M Saunders, S Sawant, C Sutantawibul, J Wilson

Baylor University, Waco, Texas, United States of America

R Bartek, A Dominguez, C Huerta Escamilla, A E Simsek, R Uniyal, A M Vargas Hernandez

Catholic University of America, Washington, DC, United States of America

B Bam, R Chudasama, S I Cooper, S V Gleyzer, C U Perez, P Rumerio82, E United States of Americai, R Yi

The University of Alabama, Tuscaloosa, Alabama, United States of America

A Akpinar, D Arcaro, C Cosby, Z Demiragli, C Erice, C Fangmeier, C Fernandez Madrazo, E Fontanesi, D Gastler, F Golf, S Jeon, I Reed, J Rohlf, K Salyer, D Sperka, D Spitzbart, I Suarez, A Tsatsos, S Yuan, A G Zecchinelli

Boston University, Boston, Massachusetts, United States of America

G Benelli, X Coubez27, D Cutts, M Hadley, U Heintz, J M Hogan83, T Kwon, G Landsberg, K T Lau, D Li, J Luo, S Mondal, M Narain, N Pervan, S Sagir84, F Simpson, M Stamenkovic, W Y Wong, X Yan, W Zhang

Brown University, Providence, Rhode Island, United States of America

S Abbott, J Bonilla, C Brainerd, R Breedon, M Calderon De La Barca Sanchez, M Chertok, M Citron, J Conway, P.T Cox, R Erbacher, F Jensen, O Kukral, G Mocellin, M Mulhearn, D Pellett, W Wei, Y Yao, F Zhang

University of California, Davis, Davis, California, United States of America

M Bachtis, R Cousins, A Datta, G Flores Avila, J Hauser, M Ignatenko, M A Iqbal, T Lam, E Manca, A Nunez Del Prado, D Saltzberg, V Valuev

University of California, Los Angeles, California, United States of America

R Clare, J W Gary, M Gordon, G Hanson, W Si, S Wimpenny

University of California, Riverside, Riverside, California, United States of America

J.G Branson, S Cittolin, S Cooperstein, D Diaz, J Duarte, L Giannini, J Guiang, R Kansal, V Krutelyov, R Lee, J Letts, M Masciovecchio, F Mokhtar, S Mukherjee, M Pieri, M Quinnan, B V Sathia Narayanan, V Sharma, M Tadel, E Vourliotis, F Würthwein, Y Xiang, A Yagil

University of California, San Diego, La Jolla, California, United States of America

A Barzdukas, L Brennan, C Campagnari, A Dorsett, J Incandela, J Kim, A J Li, P Masterson, H Mei, J Richman, U Sarica, R Schmitz, F Setti, J Sheplock, D Stuart, T Á Vámi, S Wang

University of California, Santa Barbara - Department of Physics, Santa Barbara, California, United States of America

A Bornheim, O Cerri, A Latorre, J Mao, H B Newman, M Spiropulu, J.R Vlimant, C Wang, S Xie, R.Y Zhu

California Institute of Technology, Pasadena, California, United States of America

J Alison, S An, M B Andrews, P Bryant, M Cremonesi, V Dutta, T Ferguson, A Harilal, C Liu, T Mudholkar, S Murthy, P Palit, M Paulini, A Roberts, A Sanchez, W Terrill

Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America

J P Cumalat, W T Ford, A Hart, A Hassani, G Karathanasis, E MacDonald, N Manganelli, A Perloff, C Savard, N Schonbeck, K Stenson, K A Ulmer, S R Wagner, N Zipper

University of Colorado Boulder, Boulder, Colorado, United States of America

J Alexander, S Bright-Thonney, X Chen, D J Cranshaw, J Fan, X Fan, D Gadkari, S Hogan, P Kotamnives, J Monroy, M Oshiro, J R Patterson, J Reichert, M Reid, A Ryd, J Thom, P Wittich, R Zou

Cornell University, Ithaca, New York, United States of America

M Albrow, M Alyari, O Amram, G Apollinari, A Apresyan, L A T Bauerdick, D Berry, J Berryhill, P C Bhat, K Burkett, J N Butler, A Canepa, G B Cerati, H W K Cheung, F Chlebana, G Cummings, J Dickinson, I Dutta, V D Elvira, Y Feng, J Freeman, A Gandrakota, Z Gecse, L Gray, D Green, A Grummer, S Grünendahl, D Guerrero, O Gutsche, R M Harris, R Heller, T C Herwig, J Hirschauer, L Horyn, B Jayatilaka, S Jindariani, M Johnson, U Joshi, T Klijnsma, B Klima, K H.M Kwok, S Lammel, D Lincoln, R Lipton, T Liu, C Madrid, K Maeshima, C Mantilla, D Mason, P McBride, P Merkel, S Mrenna, S Nahn, J Ngadiuba, D Noonan, V Papadimitriou, N Pastika, K Pedro, C Pena85, F Ravera, A Reinsvold Hall86, L Ristori, E Sexton-Kennedy, N Smith, A Soha, L Spiegel, S Stoynev, J Strait, L Taylor, S Tkaczyk, N V Tran, L Uplegger, E W Vaandering, I Zoi

Fermi National Accelerator Laboratory, Batavia, Illinois, United States of America

C Aruta, P Avery, D Bourilkov, L Cadamuro, P Chang, V Cherepanov, R D Field, E Koenig, M Kolosova, J Konigsberg, A Korytov, K H Lo, K Matchev, N Menendez, G Mitselmakher, K Mohrman, A Muthirakalayil Madhu, N Rawal, D Rosenzweig, S Rosenzweig, K Shi, J Wang

University of Florida, Gainesville, Florida, United States of America

T Adams, A Al Kadhim, A Askew, S Bower, R Habibullah, V Hagopian, R Hashmi, R.S Kim, S Kim, T Kolberg, G Martinez, H Prosper, P R Prova, M Wulansatiti, R Yohay, J Zhang

Florida State University, Tallahassee, Florida, United States of America

B Alsufyani, M M Baarmand, S Butalla, T Elkafrawy20, M Hohlmann, R Kumar Verma, M Rahmani, E Yanes

Florida Institute of Technology, Melbourne, Florida, United States of America

M R Adams, A Baty, C Bennett, R Cavanaugh, R Escobar Franco, O Evdokimov, C E Gerber, D J Hofman, J h Lee, D S Lemos, A H Merrit, C Mills, S Nanda, G Oh, B Ozek, D Pilipovic, R Pradhan, T Roy, S Rudrabhatla, M B Tonjes, N Varelas, Z Ye, J Yoo

University of Illinois Chicago, Chicago, United States of America, Chicago, United States of America

M Alhusseini, D Blend, K Dilsiz87, L Emediato, G Karaman, O K Köseyan, J -P Merlo, A Mestvirishvili88, J Nachtman, O Neogi, H Ogul89, Y Onel, A Penzo, C Snyder, E Tiras90

The University of Iowa, Iowa City, Iowa, United States of America

B Blumenfeld, L Corcodilos, J Davis, A V Gritsan, L Kang, S Kyriacou, P Maksimovic, M Roguljic, J Roskes, S Sekhar, M Swartz

Johns Hopkins University, Baltimore, Maryland, United States of America

A Abreu, L F Alcerro Alcerro, J Anguiano, P Baringer, A Bean, Z Flowers, D Grove, J King, G Krintiras, M Lazarovits, C Le Mahieu, C Lindsey, J Marquez, N Minafra, M Murray, M Nickel, M Pitt, S Popescu91, C Rogan, C Royon, R Salvatico, S Sanders, C Smith, Q Wang, G Wilson

The University of Kansas, Lawrence, Kansas, United States of America

B Allmond, A Ivanov, K Kaadze, A Kalogeropoulos, D Kim, Y Maravin, K Nam, J Natoli, D Roy, G Sorrentino

Kansas State University, Manhattan, Kansas, United States of America

F Rebassoo, D Wright

Lawrence Livermore National Laboratory, Livermore, California, United States of America

A Baden, A Belloni, Y M Chen, S C Eno, N J Hadley, S Jabeen, R G Kellogg, T Koeth, Y Lai, S Lascio, A C Mignerey, S Nabili, C Palmer, C Papageorgakis, M M Paranjpe, L Wang

University of Maryland, College Park, Maryland, United States of America

J Bendavid, I A Cali, M D'Alfonso, J Eysermans, C Freer, G Gomez-Ceballos, M Goncharov, G Grosso, P Harris, D Hoang, D Kovalskyi, J Krupa, L Lavezzo, Y -J Lee, K Long, C Mironov, A Novak, C Paus, D Rankin, C Roland, G Roland, S Rothman, G S F Stephans, Z Wang, B Wyslouch, T J Yang

Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America

B Crossman, B M Joshi, C Kapsiak, M Krohn, D Mahon, J Mans, B Marzocchi, S Pandey, M Revering, R Rusack, R Saradhy, N Schroeder, N Strobbe, M A Wadud

University of Minnesota, Minneapolis, Minnesota, United States of America

L M Cremaldi

University of Mississippi, Oxford, Mississippi, United States of America

K Bloom, D R Claes, G Haza, J Hossain, C Joo, I Kravchenko, J E Siado, W Tabb, A Vagnerini, A Wightman, F Yan, D Yu

University of Nebraska-Lincoln, Lincoln, Nebraska, United States of America

H Bandyopadhyay, L Hay, I Iashvili, A Kharchilava, M Morris, D Nguyen, S Rappoccio, H Rejeb Sfar, A Williams

State University of New York at Buffalo, Buffalo, New York, United States of America

G Alverson, E Barberis, J Dervan, Y Haddad, Y Han, A Krishna, J Li, M Lu, G Madigan, R Mccarthy, D.M Morse, V Nguyen, T Orimoto, A Parker, L Skinnari, A Tishelman-Charny, B Wang, D Wood

Northeastern University, Boston, Massachusetts, United States of America

S Bhattacharya, J Bueghly, Z Chen, S Dittmer, K A Hahn, Y Liu, Y Miao, D G Monk, M H Schmitt, A Taliercio, M Velasco

Northwestern University, Evanston, Illinois, United States of America

G Agarwal, R Band, R Bucci, S Castells, A Das, R Goldouzian, M Hildreth, K W Ho, K Hurtado Anampa, T Ivanov, C Jessop, K Lannon, J Lawrence, N Loukas, L Lutton, J Mariano, N Marinelli, I Mcalister, T McCauley, C Mcgrady, C Moore, Y Musienko16, H Nelson, M Osherson, A Piccinelli, R Ruchti, A Townsend, Y Wan, M Wayne, H Yockey, M Zarucki, L Zygala

University of Notre Dame, Notre Dame, Indiana, United States of America

A Basnet, B Bylsma, M Carrigan, L S Durkin, C Hill, M Joyce, M Nunez Ornelas, K Wei, B.L Winer, B R Yates

The Ohio State University, Columbus, Ohio, United States of America

F M Addesa, H Bouchamaoui, P Das, G Dezoort, P Elmer, A Frankenthal, B Greenberg, N Haubrich, G Kopp, S Kwan, D Lange, A Loeliger, D Marlow, I Ojalvo, J Olsen, A Shevelev, D Stickland, C Tully

Princeton University, Princeton, New Jersey, United States of America

S Malik

University of Puerto Rico, Mayaguez, Puerto Rico, United States of America

A S Bakshi, V E Barnes, S Chandra, R Chawla, S Das, A Gu, L Gutay, M Jones, A W Jung, D Kondratyev, A M Koshy, M Liu, G Negro, N Neumeister, G Paspalaki, S Piperov, V Scheurer, J F Schulte, M Stojanovic, J Thieman, A K Virdi, F Wang, W Xie

Purdue University, West Lafayette, Indiana, United States of America

J Dolen, N Parashar, A Pathak

Purdue University Northwest, Hammond, Indiana, United States of America

D Acosta, T Carnahan, K M Ecklund, P J Fernández Manteca, S Freed, P Gardner, F J M Geurts, W Li, O Miguel Colin, B P Padley, R Redjimi, J Rotter, E Yigitbasi, Y Zhang

Rice University, Houston, Texas, United States of America

A Bodek, P de Barbaro, R Demina, J L Dulemba, A Garcia-Bellido, O Hindrichs, A Khukhunaishvili, N Parmar, P Parygin92, E Popova92, R Taus

University of Rochester, Rochester, New York, United States of America

K Goulianos

The Rockefeller University, New York, New York, United States of America

B Chiarito, J P Chou, Y Gershtein, E Halkiadakis, M Heindl, D Jaroslawski, O Karacheban30, I Laflotte, A Lath, R Montalvo, K Nash, H Routray, S Salur, S Schnetzer, S Somalwar, R Stone, S A Thayil, S Thomas, J Vora, H Wang

Rutgers, The State University of New Jersey, Piscataway, New Jersey, United States of America

H Acharya, D Ally, A G Delannoy, S Fiorendi, S Higginbotham, T Holmes, A R Kanuganti, N Karunarathna, L Lee, E Nibigira, S Spanier

University of Tennessee, Knoxville, Tennessee, United States of America

D Aebi, M Ahmad, O Bouhali93, R Eusebi, J Gilmore, T Huang, T Kamon94, H Kim, S Luo, R Mueller, D Overton, D Rathjens, A Safonov

Texas A&M University, College Station, Texas, United States of America

N Akchurin, J Damgov, V Hegde, A Hussain, Y Kazhykarim, K Lamichhane, S W Lee, A Mankel, T Peltola, I Volobouev, A Whitbeck

Texas Tech University, Lubbock, Texas, United States of America

E Appelt, Y Chen, S Greene, A Gurrola, W Johns, R Kunnawalkam Elayavalli, A Melo, F Romeo, P Sheldon, S Tuo, J Velkovska, J Viinikainen

Vanderbilt University, Nashville, Tennessee, United States of America

B Cardwell, B Cox, J Hakala, R Hirosky, A Ledovskoy, C Neu, C E Perez Lara

University of Virginia, Charlottesville, Virginia, United States of America

P E Karchin

Wayne State University, Detroit, Michigan, United States of America

A Aravind, S Banerjee, K Black, T Bose, S Dasu, I De Bruyn, P Everaerts, C Galloni, H He, M Herndon, A Herve, C K Koraka, A Lanaro, R Loveless, J Madhusudanan Sreekala, A Mallampalli, A Mohammadi, S Mondal, G Parida, L Pétré, D Pinna, A Savin, V Shang, V Sharma, W H Smith, D Teague, H.F Tsoi, W Vetens, A Warden

University of Wisconsin - Madison, Madison, Wisconsin, United States of America

S Afanasiev, V Andreev, Yu Andreev, T Aushev, M Azarkin, A Babaev, A Belyaev, V Blinov95, E Boos, V Borshch, D Budkouski, V Bunichev, V Chekhovsky, R Chistov95, M Danilov95, A Dermenev, T Dimova95, D Druzhkin96, M Dubinin85, L Dudko, A Ershov, G Gavrilov, V Gavrilov, S Gninenko, V Golovtcov, N Golubev, I Golutvin, I Gorbunov, A Gribushin, Y Ivanov, V Kachanov, V Karjavine, A Karneyeu, V Kim95, M Kirakosyan, D Kirpichnikov, M Kirsanov, V Klyukhin, O Kodolova97, V Korenkov, A Kozyrev95, N Krasnikov, A Lanev, P Levchenko98, N Lychkovskaya, V Makarenko, A Malakhov, V Matveev95, V Murzin, A Nikitenko99,97, S Obraztsov, V Oreshkin, V Palichik, V Perelygin, S Petrushanko, S Polikarpov95, V Popov, O Radchenko95, M Savina, V Savrin, V Shalaev, S Shmatov, S Shulha, Y Skovpen95, S Slabospitskii, V Smirnov, A Snigirev, D Sosnov, V Sulimov, E Tcherniaev, A Terkulov, O Teryaev, I Tlisova, A Toropin, L Uvarov, A Uzunian, A Vorobyev, N Voytishin, B S Yuldashev100, A Zarubin, I Zhizhin, A Zhokin

Authors affiliated with an institute or an international laboratory covered by a cooperation agreement with CERN

† Deceased

1Also at Yerevan State University, Yerevan, Armenia

2Also at TU Wien, Vienna, Austria

3Also at Institute of Basic and Applied Sciences, Faculty of Engineering, Arab Academy for Science, Technology and Maritime Transport, Alexandria, Egypt

4Also at Ghent University, Ghent, Belgium

5Also at Universidade Estadual de Campinas, Campinas, Brazil

6Also at Federal University of Rio Grande do Sul, Porto Alegre, Brazil

7Also at UFMS, Nova Andradina, Brazil

8Also at Nanjing Normal University, Nanjing, People's Republic of China

9Now at The University of Iowa, Iowa City, Iowa, United States of America

10Also at University of Chinese Academy of Sciences, Beijing, People's Republic of China

11Also at People's Republic of China Center of Advanced Science and Technology, Beijing, People's Republic of China

12Also at University of Chinese Academy of Sciences, Beijing, People's Republic of China

13Also at People's Republic of China Spallation Neutron Source, Guangdong, People's Republic of China

14Now at Henan Normal University, Xinxiang, People's Republic of China

15Also at Université Libre de Bruxelles, Bruxelles, Belgium

16Also at an institute or an international laboratory covered by a cooperation agreement with CERN

17Also at Helwan University, Cairo, Egypt

18Now at Zewail City of Science and Technology, Zewail, Egypt

19Also at British University in Egypt, Cairo, Egypt

20Now at Ain Shams University, Cairo, Egypt

21Also at Purdue University, West Lafayette, Indiana, United States of America

22Also at Université de Haute Alsace, Mulhouse, France

23Also at Department of Physics, Tsinghua University, Beijing, People's Republic of China

24Also at The University of the State of Amazonas, Manaus, Brazil

25Also at Erzincan Binali Yildirim University, Erzincan, Turkey

26Also at University of Hamburg, Hamburg, Germany

27Also at RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany

28Also at Isfahan University of Technology, Isfahan, Iran

29Also at Bergische University Wuppertal (BUW), Wuppertal, Germany

30Also at Brandenburg University of Technology, Cottbus, Germany

31Also at Forschungszentrum Jülich, Juelich, Germany

32Also at CERN, European Organization for Nuclear Research, Geneva, Switzerland

33Also at Institute of Physics, University of Debrecen, Debrecen, Hungary

34Also at Institute of Nuclear Research ATOMKI, Debrecen, Hungary

35Now at Universitatea Babes-Bolyai - Facultatea de Fizica, Cluj-Napoca, Romania

36Also at Physics Department, Faculty of Science, Assiut University, Assiut, Egypt

37Also at HUN-REN Wigner Research Centre for Physics, Budapest, Hungary

38Also at Punjab Agricultural University, Ludhiana, India

39Also at University of Visva-Bharati, Santiniketan, India

40Also at Indian Institute of Science (IISc), Bangalore, India

41Also at Birla Institute of Technology, Mesra, Mesra, India

42Also at IIT Bhubaneswar, Bhubaneswar, India

43Also at Institute of Physics, Bhubaneswar, India

44Also at University of Hyderabad, Hyderabad, India

45Also at Deutsches Elektronen-Synchrotron, Hamburg, Germany

46Also at Department of Physics, Isfahan University of Technology, Isfahan, Iran

47Also at Sharif University of Technology, Tehran, Iran

48Also at Department of Physics, University of Science and Technology of Mazandaran, Behshahr, Iran

49Also at Italian National Agency for New Technologies, Energy and Sustainable Economic Development, Bologna, Italy

50Also at Centro Siciliano di Fisica Nucleare e di Struttura Della Materia, Catania, Italy

51Also at Università degli Studi Guglielmo Marconi, Roma, Italy

52Also at Scuola Superiore Meridionale, Università di Napoli 'Federico II', Napoli, Italy

53Also at Fermi National Accelerator Laboratory, Batavia, Illinois, United States of America

54Also at Consiglio Nazionale delle Ricerche - Istituto Officina dei Materiali, Perugia, Italy

55Also at Riga Technical University, Riga, Latvia

56Also at Department of Applied Physics, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, Malaysia

57Also at Consejo Nacional de Ciencia y Tecnología, Mexico City, Mexico

58Also at Trincomalee Campus, Eastern University, Sri Lanka, Nilaveli, Sri Lanka

59Also at Saegis Campus, Nugegoda, Sri Lanka

60Also at National and Kapodistrian University of Athens, Athens, Greece

61Also at Ecole Polytechnique Fédérale LaUnited States of Americanne, LaUnited States of Americanne, Switzerland

62Also at Universität Zürich, Zurich, Switzerland

63Also at Stefan Meyer Institute for Subatomic Physics, Vienna, Austria

64Also at Laboratoire d'Annecy-le-Vieux de Physique des Particules, IN2P3-CNRS, Annecy-le-Vieux, France

65Also at Near East University, Research Center of Experimental Health Science, Mersin, Turkey

66Also at Konya Technical University, Konya, Turkey

67Also at Izmir Bakircay University, Izmir, Turkey

68Also at Adiyaman University, Adiyaman, Turkey

69Also at Bozok Universitetesi Rektörlügü, Yozgat, Turkey

70Also at Marmara University, Istanbul, Turkey

71Also at Milli Savunma University, Istanbul, Turkey

72Also at Kafkas University, Kars, Turkey

73Now at stanbul Okan University, Istanbul, Turkey

74Also at Hacettepe University, Ankara, Turkey

75Also at Istanbul University - Cerrahpasa, Faculty of Engineering, Istanbul, Turkey

76Also at Yildiz Technical University, Istanbul, Turkey

77Also at Vrije Universiteit Brussel, Brussel, Belgium

78Also at School of Physics and Astronomy, University of Southampton, Southampton, United Kingdom

79Also at University of Bristol, Bristol, United Kingdom

80Also at IPPP Durham University, Durham, United Kingdom

81Also at Monash University, Faculty of Science, Clayton, Australia

82Also at Università di Torino, Torino, Italy

83Also at Bethel University, St. Paul, Minnesota, United States of America

84Also at Karamanoğlu Mehmetbey University, Karaman, Turkey

85Also at California Institute of Technology, Pasadena, California, United States of America

86Also at United States Naval Academy, Annapolis, Maryland, United States of America

87Also at Bingol University, Bingol, Turkey

88Also at Georgian Technical University, Tbilisi, Georgia

89Also at Sinop University, Sinop, Turkey

90Also at Erciyes University, Kayseri, Turkey

91Also at Horia Hulubei National Institute of Physics and Nuclear Engineering (IFIN-HH), Bucharest, Romania

92Now at an institute or an international laboratory covered by a cooperation agreement with CERN

93Also at Texas A&M University at Qatar, Doha, Qatar

94Also at Kyungpook National University, Daegu, Republic of Korea

95Also at another institute or international laboratory covered by a cooperation agreement with CERN

96Also at Universiteit Antwerpen, Antwerpen, Belgium

97Also at Yerevan Physics Institute, Yerevan, Armenia

98Also at Northeastern University, Boston, Massachusetts, United States of America

99Also at Imperial College, London, United Kingdom

100Also at Institute of Nuclear Physics of the Uzbekistan Academy of Sciences, Tashkent, Uzbekistan

Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC (2025)

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