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The ALICE Zero Degree Calorimeter system (ZDC) is composed of two identical sets of calorimeters, placed at opposite sides with respect to the interaction point, 114 meters away from it, complemented by two small forward electromagnetic calorimeters (ZEM). Each set of detectors consists of a neutron (ZN) and a proton (ZP) ZDC. They are placed at zero degrees with respect to the LHC axis and allow to detect particles emitted close to beam direction, in particular neutrons and protons emerging from hadronic heavy-ion collisions (spectator nucleons) and those emitted from electromagnetic processes. For neutrons emitted by these two processes, the ZN calorimeters have nearly 100% acceptance.
During the √sNN = 2.76 TeV Pb-Pb data-taking, the ALICE Collaboration studied forward neutron emission with a dedicated trigger, requiring a minimum energy deposition in at least one of the two ZN. By exploiting also the information of the two ZEM calorimeters it has been possible to separate the contributions of electromagnetic and hadronic processes and to study single neutron vs. multiple neutron emission.
The measured cross sections of single and mutual electromagnetic dissociation of Pb nuclei at √sNN = 2.76 TeV, with neutron emission, are σsingle EMD = 187:4 ± 0.2 (stat.)−11.2+13.2 (syst.) b and σmutual EMD = 5.7 ± 0.1 (stat.) ±0.4 (syst.) b, respectively [1]. This is the first measurement of electromagnetic dissociation of 208Pb nuclei at the LHC energies, allowing a test of electromagnetic dissociation theory in a new energy regime. The experimental results are compared to the predictions from a relativistic electromagnetic dissociation model.
Mid-rapidity transverse mass spectra and multiplicity densities of charged and neutral kaons are reported for Au + Au collisions at √sNN = 130 GeV at RHIC. The spectra are exponential in transverse mass, with an inverse slope of about 280 MeV in central collisions. The multiplicity densities for these particles scale with the negative hadron pseudo-rapidity density. The charged kaon to pion ratios are K+/π− = 0.161± 0.002(stat) ± 0.024(syst) and K−/π− = 0.146± 0.002(stat) ± 0.022(syst) for the most central collisions. The K+/π− ratio is lower than the same ratio observed at the SPS while the K−/π− is higher than the SPS result. The ratios are enhanced by about 50% relative to p + p and p¯ + p collision data at similar energies.
We present the first measurements of charge-dependent correlations on angular difference variables η1 − η2 (pseudorapidity) and φ1 − φ2 (azimuth) for primary charged hadrons with transverse momentum 0.15 <= pt <= 2 GeV/c and |η| <= 1.3 from Au–Au collisions at √sNN = 130 GeV. We observe correlation structures not predicted by theory but consistent with evolution of hadron emission geometry with increasing centrality from one-dimensional fragmentation of color strings along the beam direction to an at least two-dimensional hadronization geometry along the beam and azimuth directions of a hadron-opaque bulk medium.
We report a high precision measurement of the transverse single spin asymmetry AN at the center of mass energy √s=200 GeV in elastic proton–proton scattering by the STAR experiment at RHIC. The AN was measured in the four-momentum transfer squared t range 0.003⩽|t|⩽0.035 (GeV/c)2, the region of a significant interference between the electromagnetic and hadronic scattering amplitudes. The measured values of AN and its t-dependence are consistent with a vanishing hadronic spin-flip amplitude, thus providing strong constraints on the ratio of the single spin-flip to the non-flip amplitudes. Since the hadronic amplitude is dominated by the Pomeron amplitude at this √s, we conclude that this measurement addresses the question about the presence of a hadronic spin flip due to the Pomeron exchange in polarized proton–proton elastic scattering.
The transverse momentum (pT) differential yields of (anti-)3He and (anti-)3H measured in p-Pb collisions at sNN−−−√ = 5.02 TeV with ALICE at the Large Hadron Collider (LHC) are presented. The ratios of the pT-integrated yields of (anti-)3He and (anti-)3H to the proton yields are reported, as well as the pT dependence of the coalescence parameters B3 for (anti-)3He and (anti-)3H. For (anti-)3He, the results obtained in four classes of the mean charged-particle multiplicity density are also discussed. These results are compared to predictions from a canonical statistical hadronization model and coalescence approaches. An upper limit on the total yield of 4He¯ is determined.
The production of K∗(892)0 and ϕ(1020) mesons in proton-proton (pp) and lead-lead (Pb-Pb) collisions at sNN−−−√=5.02 TeV has been measured using the ALICE detector at the Large Hadron Collider (LHC). The transverse momentum (pT) distributions of K∗(892)0 and ϕ(1020) mesons have been measured at midrapidity (|y|<0.5) up to pT=20 GeV/c in inelastic pp collisions and for several Pb-Pb collision centralities. The collision centrality and collision energy dependence of the average transverse momenta agree with the radial flow scenario observed with stable hadrons, showing that the effect is stronger for more central collisions and higher collision energies. The K∗0/K ratio is found to be suppressed in Pb-Pb collisions relative to pp collisions: this indicates a loss of the measured K∗(892)0 signal due to rescattering of its decay products in the hadronic phase. In contrast, for the longer-lived ϕ(1020) mesons, no such suppression is observed. The nuclear modification factors (RAA) of K∗(892)0 and ϕ(1020) mesons are calculated using pp reference spectra at the same collision energy. In central Pb-Pb collisions for pT>8 GeV/c, the RAA values of K∗(892)0 and ϕ(1020) are below unity and observed to be similar to those of pions, kaons, and (anti)protons. The RAA values at high pT (>~8 GeV/c) for K∗(892)0 and ϕ(1020) mesons are in agreement within uncertainties for sNN−−−√=5.02 and 2.76 TeV.
The production yield of the Λ(1520) baryon resonance is measured at mid-rapidity in Pb-Pb collisions at sNN−−−√ = 2.76 TeV with the ALICE detector at the LHC. The measurement is performed in the Λ(1520)→pK− (and charge conjugate) hadronic decay channel as a function of the transverse momentum (pT) and collision centrality. The pT-integrated production rate of Λ(1520) relative to Λ in central collisions is suppressed by about a factor of 2 with respect to peripheral collisions. This is the first observation of the suppression of a baryonic resonance at the LHC and the first 3σ evidence of Λ(1520) suppression within a single collision system. The measured Λ(1520)/Λ ratio in central collisions is smaller than the value predicted by the statistical hadronisation model calculations. The shape of the measured pT distribution and the centrality dependence of the suppression are reproduced by the EPOS3 Monte Carlo event generator. The measurement adds further support to the formation of a dense hadronic phase in the final stages of the evolution of the fireball created in heavy-ion collisions, lasting long enough to cause a significant reduction in the observable yield of short-lived resonances.
We report the differential charged jet cross section and jet fragmentation distributions measured with the ALICE detector in proton-proton collisions at a centre-of-mass energy s√= 7 TeV. Jets with pseudo-rapidity |η|<0.5 are reconstructed from charged particles using the anti-kT jet finding algorithm with a resolution parameter R = 0.4. The jet cross section is measured in the transverse momentum interval 5 ≤pchjetT< 100 GeV/c. Jet fragmentation is studied measuring the scaled transverse momentum spectra of the charged constituents of jets in four intervals of jet transverse momentum between 5 GeV/c and 30 GeV/c. The measurements are compared to calculations from the PYTHIA model as well as next-to-leading order perturbative QCD calculations with POWHEG + PYTHIA8. The charged jet cross section is described by POWHEG for the entire measured range of pchjetT. For pchjetT > 40 GeV/c, the PYTHIA calculations also agree with the measured charged jet cross section. PYTHIA6 simulations describe the fragmentation distributions to 15%. Larger discrepancies are observed for PYTHIA8.
The cross section of jets reconstructed from charged particles is measured in the transverse momentum range of 5<pT<100 GeV/c in pp collisions at the center-of-mass energy of s√=5.02 TeV with the ALICE detector. The jets are reconstructed using the anti-kT algorithm with resolution parameters R=0.2, 0.3, 0.4, and 0.6 in the pseudorapidity range |η|<0.9−R. The charged jet cross sections are compared with the leading order (LO) and to next-to-leading order (NLO) perturbative Quantum ChromoDynamics (pQCD) calculations. It was found that the NLO calculations agree better with the measurements. The cross section ratios for different resolution parameters were also measured. These ratios increase from low pT to high pT and saturate at high pT, indicating that jet collimation is larger at high pT than at low pT. These results provide a precision test of pQCD predictions and serve as a baseline for the measurement in Pb−Pb collisions at the same energy to quantify the effects of the hot and dense medium created in heavy-ion collisions at the LHC.
The global polarization of the Λ and Λ¯¯¯¯ hyperons is measured for Pb-Pb collisions at sNN−−−√ = 2.76 and 5.02 TeV recorded with the ALICE at the LHC. The results are reported differentially as a function of collision centrality and hyperon's transverse momentum (pT) for the range of centrality 5-50%, 0.5<pT<5 GeV/c, and rapidity |y|<0.5. The hyperon global polarization averaged for Pb-Pb collisions at sNN−−−√ = 2.76 and 5.02 TeV is found to be consistent with zero, ⟨PH⟩ (%) ≈ - 0.01 ± 0.05 (stat.) ± 0.03 (syst.) in the collision centrality range 15-50%, where the largest signal is expected. The results are compatible with expectations based on an extrapolation from measurements at lower collision energies at RHIC, hydrodynamical model calculations, and empirical estimates based on collision energy dependence of directed flow, all of which predict the global polarization values at LHC energies of the order of 0.01%.
The production of K∗(892)0 and ϕ(1020) in pp collisions at s√ = 8 TeV was measured using Run 1 data collected by the ALICE collaboration at the LHC. The pT-differential yields d2N/dydpT in the range 0<pT<20 GeV/c for K∗0 and 0.4<pT<16 GeV/c for ϕ have been measured at midrapidity, |y|<0.5. Moreover, improved measurements of the K∗(892)0 and ϕ(1020) at s√=7TeV are presented. The collision energy dependence of pT distributions, pT-integrated yields and particle ratios in inelastic pp collisions are examined. The results are also compared with different collision systems. The values of the particle ratios are found to be similar to those measured at other LHC energies. In pp collisions a hardening of the particle spectra is observed with increasing energy, but at the same time it is also observed that the relative particle abundances are independent of the collision energy. The pT-differential yields of K∗0 and ϕ in pp collisions at s√=8 TeV are compared with the expectations of different Monte Carlo event generators.
The differential charged jet cross sections, jet fragmentation distributions, and jet shapes are measured in minimum bias proton-proton collisions at centre-of-mass energy s√=7 TeV using the ALICE detector at the LHC. Jets are reconstructed from charged particle momenta in the mid-rapidity region using the sequential recombination kT and anti-kT as well as the SISCone jet finding algorithms with several resolution parameters in the range R=0.2 to 0.6. Differential jet production cross sections measured with the three jet finders are in agreement in the transverse momentum (pT) interval 20<pjet,chT<100 GeV/c. They are also consistent with prior measurements carried out at the LHC by the ATLAS collaboration. The jet charged particle multiplicity rises monotonically with increasing jet pT, in qualitative agreement with prior observations at lower energies. The transverse profiles of leading jets are investigated using radial momentum density distributions as well as distributions of the average radius containing 80% (⟨R80⟩) of the reconstructed jet pT. The fragmentation of leading jets with R=0.4 using scaled pT spectra of the jet constituents is studied. The measurements are compared to model calculations from event generators (PYTHIA, PHOJET, HERWIG). The measured radial density distributions and ⟨R80⟩ distributions are well described by the PYTHIA model (tune Perugia-2011). The fragmentation distributions are better described by HERWIG.
Correction to: Nature https://doi.org/10.1038/s41586-020-3001-6Published online 09 December 2020
In Fig. 1c of this Article, owing to an error during the production process, the equation incorrectly began ‘C(k*, r*) = …’ instead of ‘C(k*) = …’. In addition, in affiliation 71 ‘Dipartimento di Fisica dell’Università degli studi di Bari Aldo Moro’ has been corrected to read ‘Dipartimento di Fisica dell’Università degli studi di Cagliari’. The original Article has been corrected online.
The production cross section of prompt Λ+c charm baryons was measured with the ALICE detector at the LHC at midrapidity in proton-proton (pp) and proton-lead (p-Pb) collisions at a centre-of-mass energy per nucleon pair of sNN−−−√=5.02 TeV. The Λ+c and Λ¯¯¯¯−c baryons were reconstructed in the hadronic decay channels Λ+c→pK−π+ and Λ+c→pK0S and respective charge conjugates. The measured differential cross sections as a function of transverse momentum (pT) and the pT-integrated Λ+c production cross section in pp and in p-Pb collisions are presented. The Λ+c nuclear modification factor (RpPb), calculated from the cross sections in pp and in p-Pb collisions, is presented and compared with the RpPb of D mesons. The Λ+c/D0 ratio is also presented and compared with the light-flavour baryon-to-meson ratios p/π and Λ/K0S, and measurements from other LHC experiments. The results are compared to predictions from model calculations and Monte Carlo event generators.
We report the first results of elliptic (v2), triangular (v3) and quadrangular flow (v4) of charged particles in Pb-Pb collisions at sNN−−−√=5.02 TeV with the ALICE detector at the CERN Large Hadron Collider. The measurements are performed in the central pseudorapidity region |η|<0.8 and for the transverse momentum range 0.2<pT<5 GeV/c. The anisotropic flow is measured using two-particle correlations with a pseudorapidity gap greater than one unit and with the multi-particle cumulant method. Compared to results from Pb-Pb collisions at sNN−−−√=2.76 TeV, the anisotropic flow coefficients v2, v3 and v4 are found to increase by (3.0±0.6)%, (4.3±1.4)% and (10.2±3.8)%, respectively, in the centrality range 0-50%. This increase can be attributed mostly to an increase of the average transverse momentum between the two energies. The measurements are found to be compatible with hydrodynamic model calculations. This comparison provides a unique opportunity to test the validity of the hydrodynamic picture and the power to further discriminate between various possibilities for the temperature dependence of shear viscosity to entropy density ratio of the produced matter in heavy-ion collisions at the highest energies.
In two-particle angular correlation measurements, jets give rise to a near-side peak, formed by particles associated to a higher pT trigger particle. Measurements of these correlations as a function of pseudorapidity (Δη) and azimuthal (Δφ) differences are used to extract the centrality and pT dependence of the shape of the near-side peak in the pT range 1<pT< 8 GeV/c in Pb-Pb and pp collisions at sNN−−−√ = 2.76 TeV. A combined fit of the near-side peak and long-range correlations is applied to the data and the peak shape is quantified by the variance of the distributions. While the width of the peak in the Δφ direction is almost independent of centrality, a significant broadening in the Δη direction is found from peripheral to central collisions. This feature is prominent for the low pT region and vanishes above 4 GeV/c. The widths measured in peripheral collisions are equal to those in pp in the Δφ direction and above 3 GeV/c in the Δη direction. Furthermore, for the 10\% most central collisions and 1<pT,assoc< 2 GeV/c, 1<pT,trig< 3 GeV/c a departure from a Gaussian shape is found: a depletion develops around the centre of the peak. The results are compared to AMPT model simulations as well as other theoretical calculations indicating that the broadening and the development of the depletion is connected to the strength of radial and longitudinal flow.
We report the results of the femtoscopic analysis of pairs of identical pions measured in p-Pb collisions at sNN−−−√=5.02 TeV. Femtoscopic radii are determined as a function of event multiplicity and pair momentum in three spatial dimensions. As in the pp collision system, the analysis is complicated by the presence of sizable background correlation structures in addition to the femtoscopic signal. The radii increase with event multiplicity and decrease with pair transverse momentum. When taken at comparable multiplicity, the radii measured in p-Pb collisions, at high multiplicity and low pair transverse momentum, are 10-20% higher than those observed in pp collisions but below those observed in A-A collisions. The results are compared to hydrodynamic predictions at large event multiplicity as well as discussed in the context of calculations based on gluon saturation.
The polarization of Λ and Λ¯ hyperons along the beam direction has been measured relative to the second and third harmonic event planes in isobar Ru+Ru and Zr+Zr collisions at √sNN = 200 GeV. This is the first experimental evidence of the hyperon polarization by the triangular flow originating from the initial density fluctuations. The amplitudes of the sine modulation for the second and third harmonic results are comparable in magnitude, increase from central to peripheral collisions, and show a mild pT dependence. The azimuthal angle dependence of the polarization follows the vorticity pattern expected due to elliptic and triangular anisotropic flow, and qualitatively disagree with most hydrodynamic model calculations based on thermal vorticity and shear induced contributions. The model results based on one of existing implementations of the shear contribution lead to a correct azimuthal angle dependence, but predict centrality and pT dependence that still disagree with experimental measurements. Thus, our results provide stringent constraints on the thermal vorticity and shear-induced contributions to hyperon polarization. Comparison to previous measurements at RHIC and the LHC for the second-order harmonic results shows little dependence on the collision system size and collision energy.
The inclusive production of the charm-strange baryon Ω0c is measured for the first time via its hadronic decay into Ω−π+ at midrapidity (|y|<0.5) in proton-proton (pp) collisions at the centre-of-mass energy s√=13 TeV with the ALICE detector at the LHC. The transverse momentum (pT) differential cross section multiplied by the branching ratio is presented in the interval 2<pT<12 GeV/c. The pT dependence of the Ω0c-baryon production relative to the prompt D0-meson and to the prompt Ξ0c-baryon production is compared to various models that take different hadronisation mechanisms into consideration. In the measured pT interval, the ratio of the pT-integrated cross sections of Ω0c and prompt Λ+c baryons multiplied by the Ω−π+ branching ratio is found to be larger by a factor of about 20 with a significance of about 4σ when compared to e+e− collisions.
Measurements of the production cross sections of prompt D0, D+, D∗+, D+s, Λ+c, and Ξ+c charm hadrons at midrapidity in proton−proton collisions at s√=13 TeV with the ALICE detector are presented. The D-meson cross sections as a function of transverse momentum (pT) are provided with improved precision and granularity. The ratios of pT-differential meson production cross sections based on this publication and on measurements at different rapidity and collision energy provide a constraint on gluon parton distribution functions at low values of Bjorken-x (10−5−10−4). The measurements of Λ+c (Ξ+c) baryon production extend the measured pT intervals down to pT=0(3)~GeV/c. These measurements are used to determine the charm-quark fragmentation fractions and the cc¯¯ production cross section at midrapidity (|y|<0.5) based on the sum of the cross sections of the weakly-decaying ground-state charm hadrons D0, D+, D+s, Λ+c, Ξ0c and, for the first time, Ξ+c, and of the strongly-decaying J/psi mesons. The first measurements of Ξ+c and Σ0,++c fragmentation fractions at midrapidity are also reported. A significantly larger fraction of charm quarks hadronising to baryons is found compared to e+e− and ep collisions. The cc¯¯ production cross section at midrapidity is found to be at the upper bound of state-of-the-art perturbative QCD calculations.
The ALICE Collaboration reports a differential measurement of inclusive jet suppression using pp and Pb−Pb collision data at a center-of-mass energy per nucleon-nucleon collision sNN−−−√=5.02 TeV. Charged-particle jets are reconstructed using the anti-kT algorithm with resolution parameters R= 0.2, 0.3, 0.4, 0.5, and 0.6 in pp collisions and R= 0.2, 0.4, 0.6 in central (0−10%), semi-central (30−50%), and peripheral (60−80%) Pb−Pb collisions. A novel approach based on machine learning is employed to mitigate the influence of jet background. This enables measurements of inclusive jet suppression in new regions of phase space, including down to the lowest jet pT≥40 GeV/c at R=0.6 in central Pb−Pb collisions. This is an important step for discriminating different models of jet quenching in the quark-gluon plasma. The transverse momentum spectra, nuclear modification factors, derived cross section, and nuclear modification factor ratios for different jet resolution parameters of charged-particle jets are presented and compared to model predictions. A mild dependence of the nuclear modification factor ratios on collision centrality and resolution parameter is observed. The results are compared to a variety of jet-quenching models with varying levels of agreement.
Correlations in azimuthal angle extending over a long range in pseudorapidity between particles, usually called the "ridge" phenomenon, were discovered in heavy-ion collisions, and later found in pp and p−Pb collisions. In large systems, they are thought to arise from the expansion (collective flow) of the produced particles. Extending these measurements over a wider range in pseudorapidity and final-state particle multiplicity is important to understand better the origin of these long-range correlations in small-collision systems. In this Letter, measurements of the long-range correlations in p−Pb collisions at sNN−−−√=5.02 TeV are extended to a pseudorapidity gap of Δη∼8 between particles using the ALICE, forward multiplicity detectors. After suppressing non-flow correlations, e.g., from jet and resonance decays, the ridge structure is observed to persist up to a very large gap of Δη∼8 for the first time in p−Pb collisions. This shows that the collective flow-like correlations extend over an extensive pseudorapidity range also in small-collision systems such as p−Pb collisions. The pseudorapidity dependence of the second-order anisotropic flow coefficient, v2({\eta}), is extracted from the long-range correlations. The v2(η) results are presented for a wide pseudorapidity range of −3.1<η<4.8 in various centrality classes in p−Pb collisions. To gain a comprehensive understanding of the source of anisotropic flow in small-collision systems, the v2(η) measurements are compared to hydrodynamic and transport model calculations. The comparison suggests that the final-state interactions play a dominant role in developing the anisotropic flow in small-collision systems.
The elliptic flow (v2) of D0 mesons from beauty-hadron decays (non-prompt D0) was measured in midcentral (30-50%) Pb-Pb collisions at a centre-of-mass energy per nucleon pair sNN−−−√ = 5.02 TeV with the ALICE detector at the LHC. The D0 mesons were reconstructed at midrapidity (|y|<0.8) from their hadronic decay D0→K−π+, in the transverse momentum interval 2<pT<12 GeV/c. The result indicates a positive v2 for non-prompt D0 mesons with a significance of 2.7σ. The non-prompt D0-meson v2 is lower than that of prompt non-strange D mesons with 3.2σ significance in 2<pT<8 GeV/c, and compatible with the v2 of beauty-decay electrons. Theoretical calculations of beauty-quark transport in a hydrodynamically expanding medium describe the measurement within uncertainties.
Measurements of charged-particle production in pp, p−Pb, and Pb−Pb collisions in the toward, away, and transverse regions with the ALICE detector are discussed. These regions are defined event-by-event relative to the azimuthal direction of the charged trigger particle, which is the reconstructed particle with the largest transverse momentum (ptrigT) in the range 8<ptrigT<15 GeV/c. The toward and away regions contain the primary and recoil jets, respectively; both regions are accompanied by the underlying event (UE). In contrast, the transverse region perpendicular to the direction of the trigger particle is dominated by the so-called UE dynamics, and includes also contributions from initial- and final-state radiation. The relative transverse activity classifier, RT=NTch/⟨NTch⟩, is used to group events according to their UE activity, where NTch is the charged-particle multiplicity per event in the transverse region and ⟨NTch⟩ is the mean value over the whole analysed sample. The energy dependence of the RT distributions in pp collisions at s√=2.76, 5.02, 7, and 13 TeV is reported, exploring the Koba-Nielsen-Olesen (KNO) scaling properties of the multiplicity distributions. The first measurements of charged-particle pT spectra as a function of RT in the three azimuthal regions in pp, p−Pb, and Pb−Pb collisions at sNN−−−√=5.02 TeV are also reported. Data are compared with predictions obtained from the event generators PYTHIA 8 and EPOS LHC. This set of measurements is expected to contribute to the understanding of the origin of collective-like effects in small collision systems (pp and p−Pb).
The Chiral Magnetic Wave (CMW) phenomenon is essential to provide insights into the strong interaction in QCD, the properties of the quark-gluon plasma, and the topological characteristics of the early universe, offering a deeper understanding of fundamental physics in high-energy collisions. Measurements of the charge-dependent anisotropic flow coefficients are studied in Pb-Pb collisions at center-of-mass energy per nucleon-nucleon collision sNN−−−√= 5.02 TeV to probe the CMW. In particular, the slope of the normalized difference in elliptic (v2) and triangular (v3) flow coefficients of positively and negatively charged particles as a function of their event-wise normalized number difference, is reported for inclusive and identified particles. The slope rNorm3 is found to be larger than zero and to have a magnitude similar to rNorm2, thus pointing to a large background contribution for these measurements. Furthermore, rNorm2 can be described by a blast wave model calculation that incorporates local charge conservation. In addition, using the event shape engineering technique yields a fraction of CMW (fCMW) contribution to this measurement which is compatible with zero. This measurement provides the very first upper limit for fCMW, and in the 10-60% centrality interval it is found to be 26% (38%) at 95% (99.7%) confidence level.
A newly developed observable for correlations between symmetry planes, which characterize the direction of the anisotropic emission of produced particles, is measured in Pb-Pb collisions at sNN−−−√=2.76 TeV with ALICE. This so-called Gaussian Estimator allows for the first time the study of these quantities without the influence of correlations between different flow amplitudes. The centrality dependence of various correlations between two, three and four symmetry planes is presented. The ordering of magnitude between these symmetry plane correlations is discussed and the results of the Gaussian Estimator are compared with measurements of previously used estimators. The results utilizing the new estimator lead to significantly smaller correlations than reported by studies using the Scalar Product method. Furthermore, the obtained symmetry plane correlations are compared to state-of-the-art hydrodynamic model calculations for the evolution of heavy-ion collisions. While the model predictions provide a qualitative description of the data, quantitative agreement is not always observed, particularly for correlators with significant non-linear response of the medium to initial state anisotropies of the collision system. As these results provide unique and independent information, their usage in future Bayesian analysis can further constrain our knowledge on the properties of the QCD matter produced in ultrarelativistic heavy-ion collisions.
The azimuthal (Δφ) correlation distributions between heavy-flavor decay electrons and associated charged particles are measured in pp and p−Pb collisions at sNN−−−√=5.02 TeV. Results are reported for electrons with transverse momentum 4<pT<16 GeV/c and pseudorapidity |η|<0.6. The associated charged particles are selected with transverse momentum 1<pT<7 GeV/c, and relative pseudorapidity separation with the leading electron |Δη|<1. The correlation measurements are performed to study and characterize the fragmentation and hadronization of heavy quarks. The correlation structures are fitted with a constant and two von Mises functions to obtain the baseline and the near- and away-side peaks, respectively. The results from p−Pb collisions are compared with those from pp collisions to study the effects of cold nuclear matter. In the measured trigger electron and associated particle kinematic regions, the two collision systems give consistent results. The Δφ distribution and the peak observables in pp and p−Pb collisions are compared with calculations from various Monte Carlo event generators.
The cross section for coherent photonuclear production of J/ψ is presented as a function of the electromagnetic dissociation (EMD) of Pb. The measurement is performed with the ALICE detector in ultra-peripheral Pb-Pb collisions at a centre-of-mass energy per nucleon pair of sNN−−−√=5.02 TeV. Cross sections are presented in five different J/ψ rapidity ranges within |y|<4, with the J/ψ reconstructed via its dilepton decay channels. In some events the J/ψ is not accompanied by EMD, while other events do produce neutrons from EMD at beam rapidities either in one or the other beam direction, or in both. The cross sections in a given rapidity range and for different configurations of neutrons from EMD allow for the extraction of the energy dependence of this process in the range 17<WγPb,n<920 GeV, where WγPb,n is the centre-of-mass energy per nucleon of the γPb system. This range corresponds to a Bjorken-x interval spanning about three orders of magnitude: 1.1×10−5<x<3.3×10−2. In addition to the ultra-peripheral and photonuclear cross sections, the nuclear suppression factor is obtained. These measurements point to a strong depletion of the gluon distribution in Pb nuclei over a broad, previously unexplored, energy range. These results, together with previous ALICE measurements, provide unprecedented information to probe quantum chromodynamics at high energies.
We report about the properties of the underlying event measured with ALICE at the LHC in pp and p−Pb collisions at sNN−−−√=5.02 TeV. The event activity, quantified by charged-particle number and summed-pT densities, is measured as a function of the leading-particle transverse momentum (ptrigT). These quantities are studied in three azimuthal-angle regions relative to the leading particle in the event: toward, away, and transverse. Results are presented for three different pT thresholds (0.15, 0.5, and 1 GeV/c) at mid-pseudorapidity (|η|<0.8). The event activity in the transverse region, which is the most sensitive to the underlying event, exhibits similar behaviour in both pp and p−Pb collisions, namely, a steep increase with ptrigT for low ptrigT, followed by a saturation at ptrigT≈5 GeV/c. The results from pp collisions are compared with existing measurements at other centre-of-mass energies. The quantities in the toward and away regions are also analyzed after the subtraction of the contribution measured in the transverse region. The remaining jet-like particle densities are consistent in pp and p−Pb collisions for ptrigT>10 GeV/c, whereas for lower ptrigT values the event activity is slightly higher in p−Pb than in pp collisions. The measurements are compared with predictions from the PYTHIA 8 and EPOS LHC Monte Carlo event generators.
Two-particle correlations with K0S, Λ/Λ¯, and charged hadrons as trigger particles in the transverse momentum range 8<pT,trig<16 GeV/c, and associated charged particles within 1<pT,assoc<8 GeV/c, are studied at mid-rapidity in pp and central Pb-Pb collisions at a centre-of-mass energy per nucleon-nucleon collision sNN−−−√=5.02 TeV with the ALICE detector at the LHC. After subtracting the contributions of the flow background, the per-trigger yields are extracted on both the near and away sides, and the ratio in Pb-Pb collisions with respect to pp collisions (IAA) is computed. The per-trigger yield in Pb-Pb collisions on the away side is strongly suppressed to the level of IAA≈0.6 for pT,assoc>3 GeV/c as expected from strong in-medium energy loss, while an enhancement develops at low pT,assoc on both the near and away sides, reaching IAA≈1.8 and 2.7 respectively. These findings are in good agreement with previous ALICE measurements from two-particle correlations triggered by neutral pions (π0-h) and charged hadrons (h-h) in Pb-Pb collisions at sNN−−−√=2.76 TeV. Moreover, the correlations with K0S mesons and Λ/Λ¯ baryons as trigger particles are compared to those of inclusive charged hadrons. The results are compared with the predictions of Monte Carlo models.
The first measurement of the e+e− pair production at low lepton pair transverse momentum (pT,ee) and low invariant mass (mee) in non-central Pb−Pb collisions at sNN−−−√=5.02 TeV at the LHC is presented. The dielectron production is studied with the ALICE detector at midrapidity (|ηe|<0.8) as a function of invariant mass (0.4≤mee<2.7 GeV/c2) in the 50−70% and 70−90% centrality classes for pT,ee<0.1 GeV/c, and as a function of pT,ee in three mee intervals in the most peripheral Pb−Pb collisions. Below a pT,ee of 0.1 GeV/c, a clear excess of e+e− pairs is found compared to the expectations from known hadronic sources and predictions of thermal radiation from the medium. The mee excess spectra are reproduced, within uncertainties, by different predictions of the photon−photon production of dielectrons, where the photons originate from the extremely strong electromagnetic fields generated by the highly Lorentz-contracted Pb nuclei. Lowest-order quantum electrodynamic (QED) calculations, as well as a model that takes into account the impact-parameter dependence of the average transverse momentum of the photons, also provide a good description of the pT,ee spectra. The measured ⟨p2T,ee⟩−−−−−√ of the excess pT,ee spectrum in peripheral Pb−Pb collisions is found to be comparable to the values observed previously at RHIC in a similar phase-space region.
Elliptic flow of heavy-flavor decay electrons in Au+Au collisions at √sNN = 27 and 54.4 GeV at RHIC
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We report on new measurements of elliptic flow (v2) of electrons from heavy-flavor hadron decays at mid-rapidity (|y|<0.8) in Au+Au collisions at sNN−−−√ = 27 and 54.4 GeV from the STAR experiment. Heavy-flavor decay electrons (eHF) in Au+Au collisions at sNN−−−√ = 54.4 GeV exhibit a non-zero v2 in the transverse momentum (pT) region of pT< 2 GeV/c with the magnitude comparable to that at sNN−−−√=200 GeV. The measured eHF v2 at 54.4 GeV is also consistent with the expectation of their parent charm hadron v2 following number-of-constituent-quark scaling as other light and strange flavor hadrons at this energy. These suggest that charm quarks gain significant collectivity through the evolution of the QCD medium and may reach local thermal equilibrium in Au+Au collisions at sNN−−−√=54.4 GeV. The measured eHF v2 in Au+Au collisions at sNN−−−√= 27 GeV is consistent with zero within large uncertainties. The energy dependence of v2 for different flavor particles (π,ϕ,D0/eHF) shows an indication of quark mass hierarchy in reaching thermalization in high-energy nuclear collisions.
Density fluctuations near the QCD critical point can be probed via an intermittency analysis in relativistic heavy-ion collisions. We report the first measurement of intermittency in Au+Au collisions at √sNN = 7.7-200 GeV measured by the STAR experiment at the Relativistic Heavy Ion Collider (RHIC). The scaled factorial moments of identified charged hadrons are analyzed at mid-rapidity and within the transverse momentum phase space. We observe a power-law behavior of scaled factorial moments in Au+Au collisions and a decrease in the extracted scaling exponent (ν) from peripheral to central collisions. The ν is consistent with a constant for different collisions energies in the mid-central (10-40%) collisions. Moreover, the ν in the 0-5% most central Au+Au collisions exhibits a non-monotonic energy dependence that reaches a minimum around √sNN = 27 GeV. The physics implications on the QCD phase structure are discussed.
The linear and mode-coupled contributions to higher-order anisotropic flow are presented for Au+Au collisions at √sN N = 27, 39, 54.4, and 200 GeV and compared to similar measurements for Pb+Pb collisions at the Large Hadron Collider (LHC). The coefficients and the flow harmonics’ correlations, which characterize the linear and mode-coupled response to the lower-order anisotropies, indicate a beam energy dependence consistent with an influence from the specific shear viscosity (η/s). In contrast, the dimensionless coefficients, mode-coupled response coefficients, and normalized symmetric cumulants are approximately beam-energy independent, consistent with a significant role from initialstate effects. These measurements could provide unique supplemental constraints to (i) distinguish between different initial-state models and (ii) delineate the temperature (T ) and baryon chemical potential (μB ) dependence of the specific shear viscosity η s (T ,μB ).
We report high-precision measurements of the longitudinal double-spin asymmetry, 𝐴𝐿𝐿, for midrapidity inclusive jet and dijet production in polarized 𝑝𝑝 collisions at a center-of-mass energy of √𝑠=200 GeV. The new inclusive jet data are sensitive to the gluon helicity distribution, Δ𝑔(𝑥,𝑄2), for gluon momentum fractions in the range from 𝑥≃0.05 to 𝑥≃0.5, while the new dijet data provide further constraints on the 𝑥 dependence of Δ𝑔(𝑥,𝑄2). The results are in good agreement with previous measurements at √𝑠=200 GeV and with recent theoretical evaluations of prior world data. Our new results have better precision and thus strengthen the evidence that Δ𝑔(𝑥,𝑄2) is positive for 𝑥>0.05.
The STAR Collaboration reports measurements of the transverse single-spin asymmetry (TSSA) of inclusive 𝜋0 at center-of-mass energies (√𝑠) of 200 GeV and 500 GeV in transversely polarized proton-proton collisions in the pseudo-rapidity region 2.7 to 4.0. The results at the two different energies show a continuous increase of the TSSA with Feynman-𝑥, and, when compared to previous measurements, no dependence on √𝑠 from 19.4 GeV to 500 GeV is found. To investigate the underlying physics leading to this large TSSA, different topologies have been studied. 𝜋0 with no nearby particles tend to have a higher TSSA than inclusive 𝜋0. The TSSA for inclusive electromagnetic jets, sensitive to the Sivers effect in the initial state, is substantially smaller, but shows the same behavior as the inclusive 𝜋0 asymmetry as a function of Feynman-𝑥. To investigate final-state effects, the Collins asymmetry of 𝜋0 inside electromagnetic jets has been measured. The Collins asymmetry is analyzed for its dependence on the 𝜋0 momentum transverse to the jet thrust axis and its dependence on the fraction of jet energy carried by the 𝜋0. The asymmetry was found to be small in each case for both center-of-mass energies. All the measurements are compared to QCD-based theoretical calculations for transverse-momentum-dependent parton distribution functions and fragmentation functions. Some discrepancies are found, which indicates new mechanisms might be involved.
Measurement of inclusive J/ψ polarization in p + p collisions at √s=200 GeV by the STAR experiment
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We report on new measurements of inclusive 𝐽/𝜓 polarization at midrapidity in 𝑝+𝑝 collisions at √𝑠=200 GeV by the STAR experiment at the Relativistic Heavy Ion Collider. The polarization parameters, 𝜆𝜃, 𝜆𝜙, and 𝜆𝜃𝜙, are measured as a function of transverse momentum (𝑝T) in both the helicity and Collins-Soper (CS) reference frames within 𝑝T<10 GeV/𝑐. Except for 𝜆𝜃 in the CS frame at the highest measured 𝑝T, all three polarization parameters are consistent with 0 in both reference frames without any strong 𝑝T dependence. Several model calculations are compared with data, and the one using the Color Glass Condensate effective field theory coupled with nonrelativistic QCD gives the best overall description of the experimental results, even though other models cannot be ruled out due to experimental uncertainties.
The STAR Collaboration at the Relativistic Heavy Ion Collider reports the first measurement of inclusive jet production in peripheral and central Au+Au collisions at √𝑠𝑁𝑁=200 GeV. Jets are reconstructed with the anti-𝑘𝑇 algorithm using charged tracks with pseudorapidity |𝜂|<1.0 and transverse momentum 0.2<𝑝ch
𝑇,jet<30 GeV/𝑐, with jet resolution parameter 𝑅=0.2, 0.3, and 0.4. The large background yield uncorrelated with the jet signal is observed to be dominated by statistical phase space, consistent with a previous coincidence measurement. This background is suppressed by requiring a high-transverse-momentum (high-𝑝𝑇) leading hadron in accepted jet candidates. The bias imposed by this requirement is assessed, and the 𝑝𝑇 region in which the bias is small is identified. Inclusive charged-particle jet distributions are reported in peripheral and central Au+Au collisions for 5<𝑝ch
𝑇,jet<25 GeV/𝑐 and 5<𝑝ch
𝑇,jet<30 GeV/𝑐, respectively. The charged-particle jet inclusive yield is suppressed for central Au+Au collisions, compared to both the peripheral Au+Au yield from this measurement and to the 𝑝𝑝 yield calculated using the PYTHIA event generator. The magnitude of the suppression is consistent with that of inclusive hadron production at high 𝑝𝑇 and that of semi-inclusive recoil jet yield when expressed in terms of energy loss due to medium-induced energy transport. Comparison of inclusive charged-particle jet yields for different values of 𝑅 exhibits no significant evidence for medium-induced broadening of the transverse jet profile for 𝑅 <0.4 in central Au+Au collisions. The measured distributions are consistent with theoretical model calculations that incorporate jet quenching.
We report new STAR measurements of the single-spin asymmetries 𝐴𝐿 for 𝑊+ and 𝑊− bosons produced in polarized proton-proton collisions at √𝑠=510 GeV as a function of the decay-positron and decay-electron pseudorapidity. The data were obtained in 2013 and correspond to an integrated luminosity of 250 pb−1. The results are combined with previous results obtained with 86 pb−1. A comparison with theoretical expectations based on polarized lepton-nucleon deep-inelastic scattering and prior polarized proton-proton data suggests a difference between the ¯𝑢 and ¯𝑑 quark helicity distributions for 0.05<𝑥<0.25. In addition, we report new results for the double-spin asymmetries 𝐴𝐿𝐿 for 𝑊±, as well as 𝐴𝐿 for 𝑍/𝛾* production and subsequent decay into electron-positron pairs.
The production of K∗(892)± meson resonance is measured at midrapidity (|y|<0.5) in Pb−Pb collisions at √sNN=5.02 TeV using the ALICE detector at the CERN Large Hadron Collider. The resonance is reconstructed via its hadronic decay channel K∗(892)±→K0Sπ±. The transverse momentum distributions are obtained for various centrality intervals in the pT range of 0.4−16 GeV/c . Measurements of integrated yields, mean transverse momenta, and particle yield ratios are reported and found to be consistent with previous ALICE measurements for K∗(892)0 within uncertainties. The pT-integrated yield ratio 2K∗(892)±/(K++K−) in central Pb−Pb collisions shows a significant suppression at a level of 9.3σ relative to pp collisions. Thermal model calculations result in an overprediction of the particle yield ratio. Although both hadron resonance gas in partial chemical equilibrium (HRG-PCE) and music + smash simulations consider the hadronic phase, only HRG-PCE accurately represents the measurements, whereas music + smash simulations tend to overpredict the particle yield ratio. These observations, along with the kinetic freeze-out temperatures extracted from the yields measured for light-flavored hadrons using the HRG-PCE model, indicate a finite hadronic phase lifetime, which decreases with increasing collision centrality percentile. The pT-differential yield ratios 2K∗(892)±/(K++K−) and 2K∗(892)±/(π++π−) are presented and compared with measurements in pp collisions at √s=5.02 TeV. Both pa rticle ratios are found to be suppressed by up to a factor of five at pT<2.0 GeV/c in central Pb−Pb collisions and are qualitatively consistent with expectations for rescattering effects in the hadronic phase. The nuclear modification factor (RAA) shows a smooth evolution with centrality and is found to be below unity at pT>8 GeV/c, consistent with measurements for other light-flavored hadrons. The smallest values are observed in most central collisions, indicating larger energy loss of partons traversing the dense medium.
A new, more precise measurement of the Λ hyperon lifetime is performed using a large data sample of Pb–Pb collisions at √sNN p ¼ 5.02 TeV with ALICE. The Λ and Λ¯ hyperons are reconstructed at midrapidity using their two-body weak decay channel Λ → p þ π− and Λ¯ → p¯ þ πþ. The measured value of the Λ lifetime is τΛ ¼ ½261.07 0.37ðstat:Þ 0.72ðsyst:Þ ps. The relative difference between the lifetime of Λ and Λ¯ , which represents an important test of CPT invariance in the strangeness sector, is also measured. The obtained value ðτΛ − τΛ¯Þ=τΛ ¼ 0.0013 0.0028ðstat:Þ 0.0021ðsyst:Þ is consistent with zero within the uncertainties. Both measurements of the Λ hyperon lifetime and of the relative difference between τΛ and τΛ¯ are in agreement with the corresponding world averages of the Particle Data Group and about a factor of three more precise.
The production of prompt +c baryons has been measured at midrapidity in the transverse momentum interval 0 < pT < 1 GeV/c for the first time, in pp and p–Pb collisions at a center-of-mass energy per nucleon-nucleon collision √sNN = 5.02 TeV. The measurement was performed in the decay channel +c → pK0S by applying new decay reconstruction techniques using a Kalman-Filter vertexing algorithm and adopting a machine-learning approach for the candidate selection. The pT -integrated +c production cross sections in both collision systems were determined and used along with the measured yields in Pb–Pb collisions to compute the pT -integrated nuclear modification factors RpPb and RAA of +c baryons, which are compared to model calculations that consider nuclear modification of the parton distribution functions. The +c /D0 baryon-to-meson yield ratio is reported for pp and p–Pb collisions. Comparisons with models that include modified hadronization processes are presented, and the implications of the results on the understanding of charm hadronization in hadronic collisions are discussed. A significant (3.7σ) modification of the mean transverse momentum of + c baryons is seen in p–Pb collisions with respect to pp collisions, while the pT -integrated +c /D0 yield ratio was found to be consistent between the two collision systems within the uncertainties.
The inclusive production of the charm-strange baryon Ω0c is measured for the first time via its semileptonic decay into Ω−e+νe at midrapidity (|y| < 0.8) in proton–proton (pp) collisions at the centre-of-mass energy √s = 13 TeV with the ALICE detector at the LHC. The transverse momentum (pT) differential cross section multiplied by the branching ratio is presented in the interval 2 < pT < 12 GeV/c. The branching-fraction ratio BR(Ω0c → Ω−e+νe)/BR(Ω0c → Ω−π+) is measured to be 1.12 ± 0.22 (stat.) ± 0.27 (syst.). Comparisons with other experimental measurements, as well as with theoretical calculations, are presented.
The measurement of the production of deuterons, tritons and 3He and their antiparticles in Pb-Pb collisions at √sNN = 5.02 TeV is presented in this article. The measurements are carried out at midrapidity (y|< 0.5) as a function of collision centrality using the ALICE detector. The pT-integrated yields, the coalescence parameters and the ratios to protons and antiprotons are reported and compared with nucleosynthesis models. The comparison of these results in different collision systems at different center-of-mass collision energies reveals a suppression of nucleus production in small systems. In the Statistical Hadronisation Model framework, this can be explained by a small correlation volume where the baryon number is conserved, as already shown in previous fluctuation analyses. However, a different size of the correlation volume is required to describe the proton yields in the same data sets. The coalescence model can describe this suppression by the fact that the wave functions of the nuclei are large and the fireball size starts to become comparable and even much smaller than the actual nucleus at low multiplicities.
The knowledge of the material budget with a high precision is fundamental for measurements of direct photon production using the photon conversion method due to its direct impact on the total systematic uncertainty. Moreover, it influences many aspects of the charged-particle reconstruction performance. In this article, two procedures to determine data-driven corrections to the material-budget description in ALICE simulation software are developed. One is based on the precise knowledge of the gas composition in the Time Projection Chamber. The other is based on the robustness of the ratio between the produced number of photons and charged particles, to a large extent due to the approximate isospin symmetry in the number of produced neutral and charged pions. Both methods are applied to ALICE data allowing for a reduction of the overall material budget systematic uncertainty from 4.5% down to 2.5%. Using these methods, a locally correct material budget is also achieved. The two proposed methods are generic and can be applied to any experiment in a similar fashion.
Long- and short-range correlations for pairs of charged particles are studied via two-particle angular correlations in pp collisions at √sNN = 13 TeV and p–Pb collisions at √s = 5.02 TeV. The correlation functions are measured as a function of relative azimuthal angle ∆φ and pseudorapidity separation ∆η for pairs of primary charged particles within the pseudorapidity interval |η| < 0.9 and the transverse-momentum interval 1 < pT < 4 GeV/c. Flow coefficients are extracted for the long-range correlations (1.6 < |∆η| < 1.8) in various high-multiplicity event classes using the low-multiplicity template fit method. The method is used to subtract the enhanced yield of away-side jet fragments in high-multiplicity events. These results show decreasing flow signals toward lower multiplicity events. Furthermore, the flow coefficients for events with hard probes, such as jets or leading particles, do not exhibit any significant changes compared to those obtained from high-multiplicity events without any specific event selection criteria. The results are compared with hydrodynamic-model calculations, and it is found that a better understanding of the initial conditions is necessary to describe the results, particularly for low-multiplicity events.
We report the first measurements of cumulants, up to 4𝑡ℎ order, of deuteron number distributions and protondeuteron correlations in Au+Au collisions recorded by the STAR experiment in phase-I of Beam Energy Scan (BES) program at the Relativistic Heavy Ion Collider. Deuteron cumulants, their ratios, and proton-deuteron mixed cumulants are presented for different collision centralities covering a range of center-of-mass energy per nucleon pair √𝑠NN = 7.7 to 200 GeV. It is found that the cumulant ratios at lower collision energies favor a canonical ensemble over a grand canonical ensemble in thermal models. An anti-correlation between proton and deuteron multiplicity is observed across all collision energies and centralities, consistent with the expectation from global baryon number conservation. The UrQMD model coupled with a phase-space coalescence mechanism qualitatively reproduces the collision-energy dependence of cumulant ratios and proton-deuteron correlations.
We report a new measurement of the production of electrons from open heavy-flavor hadron decays (HFEs) at mid-rapidity (|y| < 0.7) in Au+Au collisions at √sNN = 200 GeV. Invariant yields of HFEs are measured for the transverse momentum range of 3.5 < pT < 9 GeV/c in various configurations of the collision geometry. The HFE yields in head-on Au+Au collisions are suppressed by approximately a factor of 2 compared to that in p + p collisions scaled by the average number of binary collisions, indicating strong interactions between heavy quarks and the hot and dense medium created in heavy-ion collisions. Comparison of these results with models provides additional tests of theoretical calculations of heavy quark energy loss in the quark-gluon plasma.
We report results on an elastic cross section measurement in proton–proton collisions at a center-of-mass energy √𝑠 = 510 GeV, obtained with the Roman Pot setup of the STAR experiment at the Relativistic Heavy Ion Collider (RHIC). The elastic differential cross section is measured in the four-momentum transfer squared range 0.23 ≤ −𝑡 ≤ 0.67 GeV2. This is the only measurement of the proton-proton elastic cross section in this 𝑡 range for collision energies above the Intersecting Storage Rings (ISR) and below the Large Hadron Collider (LHC) colliders. We find that a constant slope 𝐵 does not fit the data in the aforementioned 𝑡 range, and we obtain a much better fit using a second-order polynomial for 𝐵(𝑡). This is the first measurement below the LHC energies for which the non-constant behavior 𝐵(𝑡) is observed. The 𝑡 dependence of 𝐵 is also determined using six subintervals of 𝑡 in the STAR measured 𝑡 range, and is in good agreement with the phenomenological models. The measured elastic differential cross section d𝜎∕dt agrees well with the results obtained at √𝑠 = 540 GeV for proton–antiproton collisions by the UA4 experiment. We also determine that the integrated elastic cross section within the STAR 𝑡-range is 𝜎f id el = 462.1 ± 0.9(stat.) ± 1.1(syst.) ± 11.6(scale) 𝜇b.