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(Color online) Histograms of the average transverse momentum per event for Au+Au at √ s NN = 20, 62, 130, and 200 GeV for the 5% most central collisions at each energy. Both data and mixed events are shown for each incident energy. The lines represent gamma distributions.
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We present results for two-particle transverse momentum correlations, <Delta p(t,i)Delta p(t,j)>, as a function of event centrality for Au+Au collisions at root SNN = 20, 62, 130, and 200 GeV at the BNL Relativistic Heavy Ion Collider. We observe correlations decreasing with centrality that are similar at all four incident energies. The correlation...
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We present results for two-particle transverse momentum correlations, ⟨Δpt,iΔpt,j⟩, as a function of event centrality for Au+Au collisions at √sNN=20, 62, 130, and 200 GeV at the BNL Relativistic Heavy Ion Collider. We observe correlations decreasing with centrality that are similar at all four incident energies. The correlations multiplied by the...
Citations
... Recent advances in heavy-ion collision experiments now enable the isolation of the thermal fluctuations from confounding effects, such as the initial state geometry fluctuations [28][29][30][31][32], flow contributions, and other non-thermal sources, allowing temperature fluctuations to be extracted from EbE mean transverse momentum fluctuations of final-state charged particles [27]. EbE mean transverse momentum fluctuations have been extensively measured across collision energies and systems in various heavy-ion facilities, offering a new avenue to study the QCD phase diagram [31,[33][34][35][36][37][38]. Progress in di-lepton observations also indicates that measurements of vector-meson invariant mass distributions by di-lepton decays can be used to determine the temperature of the thermal source at different ...
... Recent advances in heavy-ion collision experiments now enable the isolation of the thermal fluctuations from confounding effects, such as the initial state geometry fluctuations [28][29][30][31][32], flow contributions, and other non-thermal sources, allowing temperature fluctuations to be extracted from EbE mean transverse momentum fluctuations of final-state charged particles [27]. EbE mean transverse momentum fluctuations have been extensively measured across collision energies and systems in various heavy-ion facilities, offering a new avenue to study the QCD phase diagram [31,[33][34][35][36][37][38]. Progress in di-lepton observations also indicates that measurements of vector-meson invariant mass distributions by di-lepton decays can be used to determine the temperature of the thermal source at different stages of the system evolution [39][40][41][42]. ...
We study the temperature fluctuations in hot quantum chromodynamics (QCD) matter. A new thermodynamic state function is introduced to describe the mean transverse momentum fluctuations of charged particles in heavy-ion collisions, enabling analytic expressions for the temperature fluctuations of different orders. This formalism is applied to the QCD thermodynamics described by a 2+1 flavor low energy effective field theory within the functional renormalization group approach. It is found that the temperature fluctuations are suppressed remarkably as the matter is evolved from the phase of hadron resonance gas to the quark-gluon plasma phase with increasing temperature or baryon chemical potential, which is attributed to the significant increase of the heat capacity of matter. Furthermore, the same mechanism leads to a negative skewness in the temperature fluctuations.
... The study of event-by-event dynamical fluctuations in quantities like mean transverse momentum (⟨p T ⟩) is an essential tool to investigate the possible formation of QGP in heavy-ion collisions [1,2,4]. One of the proposed signs of the QGP formation is a non-monotonic behavior of such fluctuations as a function of centrality or incident energy [3]. ...
... However, fluctuations arising in the initial-state of the colliding nuclei also play a major role, a hint of which was obtained from the measurement by the ALICE Collaboration for Pb−Pb collisions at center-of-mass energy per nucleon √ s NN = 2.76 TeV [2]. Recent measurements by the STAR [1,6] and ALICE [2] experiment at RHIC and LHC reported that the strength of dynamical ⟨p T ⟩ fluctuations decreased * subhadeep.roy@cern.ch † tanu.gahlaut@cern.ch ...
Estimations of event-by-event mean transverse momentum () fluctuations are reported in terms of the integral correlator, , and the skewness of event-wise distribution in protonproton (pp) collisions at TeV with the Monte Carlo event generators PYTHIA8 and HERWIG7. The final-state charged particles with transverse momentum () and pseudorapidity () ranges GeV/c and were considered for the investigation. The correlator, , is observed to follow distinct decreasing trends with average charged particle multiplicity () for the models. Furthermore, both models yield positive finite skewness in low-multiplicity events. The fluctuations are additionally studied using the transverse spherocity estimator () to comprehend the relative contributions from hard scattering (jets) and other soft processes to the observed fluctuations. Comparing the model predictions would enhance our understanding of fluctuation dynamics in pp collisions, establishing a crucial baseline for studying non-trivial fluctuations in heavy-ion collisions.
... The dynamical ⟨p T ⟩ fluctuations estimated by variance have been extensively studied in the Super Proton Synchrotron (SPS) [1,[19][20][21][22], Relativistic Heavy-Ion Collider (RHIC) [2,3,[23][24][25], and the Large Hadron Collider (LHC) [4,26,27]. These results reveal a universal multiplicity dependence, where correlations are progressively diluted with increasing participant numbers, consistent with dominance by particle pairs originating from the same nucleon-nucleon collisions. ...
... GeV, as shown in panel (b) of Fig. 3, suggesting significant EbE fluctuations. An inverse dependence of variance on centrality is consistently observed across all energies, aligning with findings from the STAR and HIJING results [24]. However, the HIJING calculations show an opposite energy dependence in peripheral versus central collisions, in contrast to the consistent energy dependence observed in published STAR measurements. ...
Event-by-event mean transverse momentum fluctuations () serve as a sensitive probe of initial state overlap geometry and energy density fluctuations in relativistic heavy-ion collisions. We present a systematic investigation of fluctuations in \auau collisions at 3.0-19.6 GeV, examining their centrality and energy dependence with the framework of an improved multiphase transport (AMPT) model. The centrality dependence of the cumulants up to fourth order deviates significantly from simple powering-law scaling. Scaled cumulants are performed, with variances aligning well with the trends observed in the experimental data. Employing a two-subevent method, short-range correlations are slightly suppressed compared to the standard approach. Furthermore, baryons exhibit more pronounced fluctuations than mesons, potentially attributable to the effect of radial flow. These results provide referenced insights into the role of initial state fluctuations across different energies in heavy-ion collisions.
... Based on the perturbative view of the Lund string model, the propagating quark's energy loss is predicted to be at a rate comparable to its string constant on the order of 1 GeV/fm [9,21]. This effect is believed to be the reason behind the observed jet quenching in heavy-ion collisions at the Relativistic Heavy Ion Collider and at the Large Hadron Collider, leading to the suppression of large p T hadron production in nucleus-nucleus compared to proton-proton collisions [22,23]. ...
We report results of hyperon production in semi-inclusive deep-inelastic scattering off deuterium, carbon, iron, and lead targets obtained with the CLAS detector and the CEBAF 5.014 GeV electron beam. These results represent the first measurements of the multiplicity ratio and transverse momentum broadening as a function of the energy fraction (z) in the current and target fragmentation regions. The multiplicity ratio exhibits a strong suppression at high z and an enhancement at low z. The measured transverse momentum broadening is an order of magnitude greater than that seen for light mesons. This indicates that the propagating entity interacts very strongly with the nuclear medium, which suggests that propagation of di-quark configurations in the nuclear medium takes place at least part of the time, even at high z. The trends of these results are qualitatively described by the GiBUU transport model, particularly for the multiplicity ratios. These observations will potentially open a new era of studies of the structure of the nucleon as well as of strange baryons.
... The p T fluctuations can be quantified by its cumulants, such as mean, variance, skewness, and kurtosis. But so far, only the mean and variance have been measured experimentally [11][12][13][14][15][16]. Recently Ref. [8] predicted that the skewness of p T fluctuations should be significantly larger than expectation from the independent source scenario, and they can be used to probe nuclear deformation effects [9,17]. ...
In relativistic heavy-ion collisions, the event-by-event mean transverse momentum fluctuations are sensitive to overlap area and energy density fluctuations in the initial state. We present a framework to calculate p T fluctuations up to fourth order using standard and subevent methods, which is validated using the HIJING model. We observe a power-law dependence for cumulants of all orders as a function of charged particle multiplicity N ch, consistent with a simple independent source picture. The fluctuation in p p collisions is observed to be larger than for p+ Pb, Pb+ Pb, and Xe+ Xe collisions at the same N ch due to bias in the number of contributing sources. The short-range correlations are greatly suppressed in the subevent method in comparison to calculations based on the standard method. This paper provides a baseline for transverse momentum fluctuations without the presence of final-state effects.
... At a given collision centrality, i.e., at a fixed experimental value of the multiplicity, the value of p t is not constant, but it fluctuates on an event-by-event basis. Fluctuations of p t at a given centrality were analyzed at RHIC very shortly after the beginning of the heavy-ion program [78]. A few years later, they were eventually studied by the Krakow group in the context of modern event-by-event hydrodynamic simulations to elucidate their physical origin [79]. ...
... Each particle has a random value of p t , chosen, independently for each particle, from an underlying probability distribution, i.e., the p t spectrum, which is a measurable observable at a given collision centrality. The magnitude of the trivial statistical fluctuations can thus be evaluated from law of large numbers: where p t = 0.57 GeV [78]. This corresponds to the the relative fluctuation of the average transverse momentum originating from the simple fact that N is finite. ...
This work establishes a deep connection between two seemingly distant branches of nuclear physics: nuclear structure and relativistic heavy-ion collisions. At the heart of this connection is the recent discovery made at particle colliders that the elliptic flow of outgoing hadrons in central nucleus-nucleus collisions is strongly impacted by the quadrupole deformation of the colliding nuclear species. I review the physics of the soft sector of relativistic heavy-ion collisions, and I explain that the interpretation of elliptic flow data in central Au+Au, U+U, and Xe+Xe collisions requires a deep understanding the structure of these ions. Subsequently, I introduce a technique that permits one to isolate collision configurations in which the deformed shapes of the colliding nuclei maximally break rotational (azimuthal) symmetry in the interaction region. This allows me to construct observables that possess an unparalleled sensitivity to the quadrupole deformation of the colliding ions, and thus to conclude that nuclear experiments at high energy can be used to place new quantitative constraints on the deformation of atomic nuclei. I emphasize the great opportunities offered by potential collider experiments aimed at the systematic study of nuclear deformation across the valley of stability.
... At a given collision centrality, i.e., at a fixed experimental value of the multiplicity, the value of p t is not constant, but it fluctuates on an event-by-event basis. Fluctuations of p t at a given centrality were analyzed at RHIC very shortly after the beginning of the heavy-ion program [78]. A few years later, they were eventually studied by the Krakow group in the context of modern event-by-event hydrodynamic simulations to elucidate their physical origin [79]. ...
... Remarkably, the value κ 3 = 0.110 chosen in Fig. 5.7, and which yield an rms v 3 in good agreement with STAR preliminary data, is fully consistent with the correlation between ε 3 and v 3 shown in Fig. C.2 The fact that the coefficients κ 2 and κ 3 chosen for 238 U+ 238 U collisions are reasonable implies that the choices made for 197 Au+ 197 Au collisions, κ 2 = 0.155 and κ 3 = 0.100, are also reasonable. The κ n coefficients are damped by vis- where p t = 0.57 GeV [78]. This corresponds to the the relative fluctuation of the average transverse momentum originating from the simple fact that N is finite. ...
Collider experiments conducted atthe BNL RHIC and at the CERN LHC show thatthe the emission of particles following the interactionof two nuclei at relativistic energy is highlyanisotropic in azimuthal angle. This observationis compatible with a hydrodynamic paradigm, accordingto which the final-state hadrons are emittedfollowing the expansion of a fluidlike systemcreated in the interaction region. Withinthis paradigm, anisotropy in the emission of particlesis enhanced whenever the colliding nucleihave deformed ground states. By meansof high-quality comparisons between the predictionsof hydrodynamic models and particle colliderdata, I study the phenomenological manifestationsof the quadrupole deformation of atomicnuclei in relativistic ¹⁹⁷Au+¹⁹⁷Au, ²³⁸U+²³⁸U,and ¹²⁹Xe+¹²⁹Xe collisions. This analysis demonstratesthat a deep understanding of the structureof the colliding ions is required for the interpretationof data in high-energy experiments. RHICdata confirms in particular the well-known factthat the geometry of ²³⁸U nuclei is that of a welldeformedellipsoid, while indicating that ¹⁹⁷Au nuclei are nearly spherical, a result which is atodds with the estimates of mean-field and empiricalnuclear models. LHC data brings instead evidenceof quadrupole deformation in the groundstate of ¹²⁹Xe nuclei, ascribable to the first visiblemanifestation of shape coexistence phenomena inhigh-energy nuclear experiments. I introduce asimple method to isolate collision configurationsthat maximally break azimuthal symmetry dueto the orientation of the deformed nuclei. Thisallows me to define observables with an unprecedentedsensitivity to the deformation of the collidingspecies, thus paving the way for quantitativestudies of nuclear structure at high energy.
... where I used p t = 0.57 GeV [41]. This is the relative fluctuation of p t coming from the simple fact that N is not infinite. ...
Preliminary data by the STAR collaboration at the BNL Relativistic Heavy Ion Collider show that the elliptic flow, , and the average transverse momentum, , of final-state hadrons produced in high-multiplicity U+U collisions are negatively correlated. This observation brings experimental evidence of a significant prolate deformation, , in the colliding U nuclei. I show that a quantitative description of STAR data can be achieved within the hydrodynamic framework of heavy-ion collisions, and that thus such kind of data in the context of high-energy nuclear experiments can help constrain the quadrupole deformation of the colliding species.
... There are trivial statistical fluctuations of p t , due to the fact that the average is evaluated over a finite sample of particles, but the observed fluctuations are larger. The excess fluctuations are called dynamical fluctuations, and have been measured in Au+Au collisions at √ s NN = 200 GeV [1] and lower energies [2][3][4], and in Pb+Pb collisions at √ s NN = 2.76 TeV [5]. Dynamical p t fluctuations are thought to originate from eventto-event fluctuations at the early stage of the collision. ...
... In Sec. II we show that a hint of this positive skew can be seen in existing STAR data [2] on Au+Au collisions, while it is clearly visible in the results of event-by-event hydrodynamic simulations of Pb+Pb collisions. This constitutes a solid basis for investigating this phenomenon. ...
... VI, where we derive a generic formula relating the skewness of the E 0 distribution to the statistical properties of the initial density field in a perturbative approach [10,11]. Figure 1 displays the histogram of the distribution of p t measured by the STAR collaboration in central Au+Au collisions [2], where p t is evaluated by averaging the transverse momenta of the charged particles observed in the detector. As mentioned in the Introduction, this quantity has trivial fluctuations due to the finite number of particles, typically of order 1000, in every event. ...
We propose the skewness of mean transverse momentum, , fluctuations as a fine probe of hydrodynamic behavior in relativistic nuclear collisions. We describe how the skewness of the distribution can be analyzed experimentally, and we use hydrodynamic simulations to predict its value. We predict in particular that fluctuations have positive and nontrivial skew at a given collision centrality. We elucidate the origin of this result by deriving generic formulas relating the fluctuations of to the fluctuations of the early-time thermodynamic quantities. We thus argue that the positive skewness of fluctuations is a universal prediction of hydrodynamic models.
... Experimentally, this is obtained from a three-particle correlation introduced by Bożek [9]. Since self correlations are subtracted in the measure of the correlation coefficient (i.e., one does not correlate a particle with itself), this observable is insensitive to trivial statistical fluctuations and probes genuine dynamical fluctuations [23], due to correlations. In hydrodynamics, ρ n can be evaluated as: ...
The correlation between the mean transverse momentum of outgoing particles, , and the magnitude of anisotropic flow, , has recently been measured in Pb+Pb collisions at the CERN Large Hadron Collider, as a function of the collision centrality. We confirm the previous observation that event-by-event hydrodynamics predicts a correlation between and that is similar to that measured in data. We show that the magnitude of this correlation can be directly predicted from the initial condition of the hydrodynamic calculation, for n=2,3, if one replaces by the corresponding initial-state anisotropy, , and by the total energy per unit rapidity of the fluid at the beginning of the hydrodynamic expansion.
