Fluctuations In Heavy-ion Collisions Research Articles

Momentum-dependent flow correlations in deformed nuclei at collision energies available at the BNL Relativistic Heavy Ion Collider

Flow fluctuations in ultrarelativistic heavy-ion collisions can be probed by studying the momentum dependent correlations or the factorization-breaking coefficients between flow harmonics in separate kinematic bins (transverse momentum $p$ or pseudorapidity $\ensuremath{\eta}$). We study such factorization-breaking coefficients for collisions of deformed $^{238}\mathrm{U}+^{238}\mathrm{U}$ nuclei to see the effect of the nuclear deformation on momentum dependent coefficients. We also study momentum dependent mixed-flow correlations for the isobar collision system: $^{96}\mathrm{Ru}+^{96}\mathrm{Ru}$ and $^{96}\mathrm{Zr}+^{96}\mathrm{Zr}$, which have the same mass number but different nuclear structure, thus providing the ideal scenario to study nuclear deformation effect on such observables. We use the TRENTO $+$ MUSIC model for simulations and event-by-event analysis of those observables. We find that these momentum dependent correlation coefficients are not only excellent candidates to probe the fluctuation in heavy-ion collision, but also show significant sensitivity to the nuclear deformation.

Impact of hadronic interactions and conservation laws on cumulants of conserved charges in a dynamical model

Understanding the phase diagram of QCD by measuring fluctuations of conserved charges in heavy-ion collision is one of the main goals of the beam energy scan program at the BNL Relativistic Heavy Ion Collider (RHIC). Within this work, we calculate the role of hadronic interactions and momentum cuts on cumulants of conserved charges up to fourth order in a system in equilibrium within a hadronic transport approach (smash). In our model the net baryon, net charge, and net strangeness are perfectly conserved on an event-by-event basis and the cumulants are calculated as a function of subvolume sizes and compared to analytic expectations. We find a modification of the kurtosis due to charge annihilation processes in systems with simplified degrees of freedom. Furthermore the result of the full smash hadron gas for the net baryon and net proton number fluctuations is presented for systems with zero and finite values of baryon chemical potential. Additionally we find that due to dynamical correlations the cumulants of the net baryon number cannot easily be recovered from the net protons. Finally the influence of deuteron cluster formation on the net proton and net baryon fluctuations in a simplified system is shown. This analysis is important to better understand the relation between measurements of fluctuations in heavy-ion collisions and theoretical calculations which are often performed in a grand canonical ensemble.

Maximum Entropy Freeze-Out of Hydrodynamic Fluctuations.

We propose a general approach to freezing out fluctuations in heavy-ion collisions using the principle of maximum entropy. We find the results naturally expressed as a direct relationship between the irreducible relative correlators quantifying the deviations of hydrodynamic as well as hadron gas fluctuations from the ideal hadron gas baseline. The method also allows us to determine heretofore unknown parameters crucial for the freeze-out of fluctuations near the QCD critical point in terms of the QCD equation of state.

Exploring critical fluctuation phenomenon according to net-proton multiplicity information entropy in AMPT model

Information entropy can be used for investigating the critical fluctuation phenomenon by describing multiplicity fluctuations in heavy-ion collisions. In this study, a multiphase transport (AMPT) model in the default version (AMPT-DEF) and with the string melting (AMPT-SM) were used as event generators to simulate the Au+Au reaction at different incident energies. Owing to the influence of the distribution bin number in extracting its information entropy, two methods, i.e., data binning and weighting factors, were proposed to correct the information entropy analysis. The comparison between information entropy and kurtosis also reflects the necessity to correct the information entropy analysis. The corrected information entropy of net-proton multiplicity was analyzed in central Au+Au collisions at sNN= 4.7, 6.4, 7.7, 8.8, 11.5, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 140, 170, and 200 GeV with the impact parameter b=3 fm. The results indicated that the fluctuations of net-proton multiplicity were essentially identical at collision energies ranging from sNN= 4.7 GeV to sNN= 200 GeV in the same model. No critical fluctuation phenomenon was found in the central Au+Au collisions simulated using the AMPT models, similar to the case of the AMPT model, which does not have. Comparing the information entropy of AMPT-SM to AMPT-DEF, the effect of partonic phase leads to a bigger fluctuation, indicating that the corrected information entropy can be a useful probe to explore the phase transition. The mid-rapidity net-proton multiplicity information entropy was also calculated, and the results led to the same conclusion. The corrected information entropy may be useful for investigating critical fluctuations, which is important for exploring critical endpoint.

Fluctuations near the liquid-gas and chiral phase transitions in hadronic matter

We investigate the fluctuations of the net-baryon number density in dense hadronic matter. Chiral dynamics is modeled via the parity doublet Lagrangian, and the mean-field approximation is employed to account for chiral criticality. We focus on the qualitative properties and systematics of the second-order susceptibility of the net-baryon number density for individual positive- and negative-parity nucleons whose masses become degenerate at the chiral restoration. It is shown that the second-order susceptibility of the positive-parity state can become negative when the chiral symmetry is restored, as a natural consequence of the unique relationship of the mass to the order parameter. Moreover, we find that such negative fluctuations are indicative of approaching the critical point on the chiral phase boundary. Our results may have consequences for the interpretation of the experimental data on net-proton fluctuations in heavy-ion collisions.

Fluctuations in heavy ion collisions and global conservation effects

Subensemble is a type of statistical ensemble which is the generalization of grand canonical and canonical ensembles. The subensemble acceptance method (SAM) provides general formulas to correct the cumulants of distributions in heavy-ion collisions for the global conservation of all QCD charges. The method is applicable for an arbitrary equation of state and sufficiently large systems, such as those created in central collisions of heavy ions. The new fluctuation measures insensitive to global conservation effects are presented. The main results are illustrated in the hadron resonance gas and van der Waals fluid frameworks.

(Anti)nucleosynthesis in heavy-ion collisions and (anti)nuclei as "baryonmeter" of the collision

The production mechanism of light (anti)nuclei in heavy-ion collisions has been extensively studied experimentally and theoretically. Two competing (anti)nucleosynthesis models are typically used to describe light (anti)nuclei yields and their ratios to other hadrons in heavy-ion collisions: the statistical hadronization model (SHM) and the nucleon coalescence model. The possibility to distinguish these phenomenological models calls for new experimental observables. Given their large baryon number, light (anti)nuclei have a high sensitivity to the baryon chemical potential (μB) of the system created in the collision. In this talk, the first measurement of event-by-event antideuteron number fluctuations in heavy-ion collisions is presented and compared with expectations of the SHM and coalescence model. In addition, the antinuclei-to-nuclei ratios are used to obtain a measurement of μB in heavy-ion collisions with unprecedented precision.

Critical point particle number fluctuations from molecular dynamics

We study fluctuations of particle number in the presence of critical point by utilizing molecular dynamics simulations of the classical Lennard-Jones fluid in a periodic box. The numerical solution of the $N$-body problem naturally incorporates all correlations, exact conservation laws, and finite size effects, allowing us to study the fluctuation signatures of the critical point in a dynamical setup. We find that large fluctuations associated with the critical point are observed when measurements are performed in coordinate subspace, but, in the absence of collective flow and expansion, are essentially washed out when momentum cuts are imposed instead. We put our findings in the context of event-by-event fluctuations in heavy-ion collisions.

Performance of the MPD Detector for the Study of Strongly-Intensive Multiplicity and Transverse Momentum Fluctuations in Heavy-Ion Collisions

Performance of the MPD Detector for the Study of Strongly-Intensive Multiplicity and Transverse Momentum Fluctuations in Heavy-Ion Collisions

Statistical uncertainty estimation of higher-order cumulants with finite efficiency and its application in heavy-ion collisions

We derive the general analytical expressions for the statistical uncertainties of cumulants up to fourth order including an efficiency correction. The analytical expressions have been tested with a toy Monte Carlo model analysis. An application to the study of particle multiplicity fluctuations in heavy-ion collisions is investigated. In this derivation, a mathematical proof is given that the validity of an averaged efficiency correction and the fluctuations induced by the non-uniformity of efficiency can be eliminated. The estimation of statistical uncertainties using the analytical formulas is found to be significantly faster than the commonly used bootstrap method. The simplicity and efficiency of using the analytical formulas may be useful for massive data analysis in many fields.

Higher-order transverse momentum fluctuations in heavy-ion collisions

In relativistic heavy-ion collisions, the event-by-event mean transverse momentum fluctuations are sensitive to overlap area and energy density fluctuations in initial state. We present a framework to calculate $p_{\mathrm{T}}$ fluctuations up to $4^{\mathrm{th}}$-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 $N_{\mathrm{ch}}$, consistent with a simple independent source picture. The fluctuation in $pp$ collisions is observed to be larger than for $p+$Pb, Pb+Pb and Xe+Xe collisions at the same $N_{\mathrm{ch}}$ due to bias in number of contributing sources. The short-range correlations are greatly suppressed in subevent method in comparison to calculations based on the standard method. This study provides a baseline for transverse momentum fluctuations without the presence of final state effects.

Correcting event-by-event fluctuations in heavy-ion collisions for exact global conservation laws with the generalized subensemble acceptance method

We introduce the subensemble acceptance method 2.0 (SAM-2.0) -- a procedure to correct cumulants of a random number distribution inside a subsystem for the effect of exact global conservation of a conserved quantity to which this number is correlated, with applications to measurements of event-by-event fluctuations in heavy-ion collisions. The method expresses the corrected cumulants in terms of the cumulants inside and outside the subsystem that are not subject to the exact conservation. The derivation assumes that all probability distributions associated with the cumulants are peaked at the mean values but are otherwise of arbitrary shape. The formalism reduces to the original SAM [V. Vovchenko et al., Phys.Lett.B 811 (2020) 135868 [arXiv:2003.13905]] when applied to a coordinate space subvolume of a uniform thermal system. As the new method is restricted neither to the uniform systems nor to the coordinate space, it is applicable to fluctuations measured in heavy-ion collisions at various collision energies in different momentum space acceptances. The SAM-2.0 thus brings the experimental measurements and theoretical calculations of event-by-event fluctuations closer together, as the latter are typically performed without the account of exact global conservation.

Coupled baryon, electric charge and strangeness fluctuations in heavy-ion collisions

We present for the first time quantitative results for the coupled dynamics of second order fluctuations in the three conserved charges of QCD based on stochastic diffusion equations for a Bjorken-type expanding hadronic medium. We show that the fluctuations deviate from local equilibrium expectations which can result in important phenomenological consequences for the interpretation of experimental data.

Constraining the hadronic spectrum and repulsive interactions in a hadron resonance gas via fluctuations of conserved charges

We simultaneously incorporate two common extensions of the hadron resonance gas model, namely the addition of extra, unconfirmed resonances to the particle list and the excluded volume repulsive interactions. We emphasize the complementary nature of these two extensions and identify combinations of conserved charge susceptibilities that allow to constrain them separately. In particular, ratios of second-order susceptibilities like $\chi_{11}^{BQ}/\chi_2^B$ and $\chi_{11}^{BS}/\chi_2^B$ are sensitive only to the baryon spectrum, while fourth-to-second order ratios like $\chi_4^B/\chi_2^B$, $\chi_{31}^{BS}/\chi_{11}^{BS}$, or $\chi_{31}^{BQ}/\chi_{11}^{BQ}$ are mainly determined by repulsive interactions. Analysis of the available lattice results suggests the presence of both the extra states in the baryon-strangeness sector and the repulsive baryonic interaction, with indications that hyperons have a smaller repulsive core than non-strange baryons. The modified hadron resonance gas model presented here significantly improves the description of lattice QCD susceptibilities at chemical freeze-out and can be used for the analysis of event-by-event fluctuations in heavy-ion collisions.

Particlization of an interacting hadron resonance gas with global conservation laws for event-by-event fluctuations in heavy-ion collisions

We revisit the problem of particlization of a QCD fluid into hadrons and resonances at the end of the fluid dynamical stage in relativistic heavy-ion collisions in a context of fluctuation measurements. The existing methods sample an ideal hadron resonance gas, therefore, they do not capture the non-Poissonian nature of the grand-canonical fluctuations, expected due to QCD dynamics such as the chiral transition or QCD critical point. We address the issue by partitioning the particlization hypersurface into locally grand-canonical fireballs populating the space-time rapidity axis that are constrained by global conservation laws. The procedure allows to quantify the effect of global conservation laws, volume fluctuations, thermal smearing and resonance decays on fluctuation measurements in various rapidity acceptances, and can be used in fluid dynamical simulations of heavy-ion collisions. As a first application, we study event-by-event fluctuations in heavy-ion collisions at the LHC using an excluded volume hadron resonance gas model matched to lattice QCD susceptibilities, with a focus on (pseudo)rapidity acceptance dependence of net baryon, net proton, and net charge cumulants. We point out large differences between net proton and net baryon cumulant ratios that make direct comparisons between the two unjustified. We observe that the existing experimental data on net-charge fluctuations at the LHC shows a strong suppression relative to a hadronic description.

Skewness of mean transverse momentum fluctuations in heavy-ion collisions

We propose the skewness of mean transverse momentum, $\langle p_t \rangle$, fluctuations as a fine probe of hydrodynamic behavior in relativistic nuclear collisions. We describe how the skewness of the $\langle p_t \rangle$ distribution can be analyzed experimentally, and we use hydrodynamic simulations to predict its value. We predict in particular that $\langle p_t \rangle$ fluctuations have positive skew, which is significantly larger than if particles were emitted independently. We elucidate the origin of this result by deriving generic formulas relating the fluctuations of $\langle p_t \rangle$ to the fluctuations of the early-time thermodynamic quantities. We postulate that the large positive skewness of $\langle p_t \rangle$ fluctuations is a generic prediction of hydrodynamic models.

Exploring the QCD Phase Diagram with Fluctuations

We report on recent progress concerning theoretical description of event-by-event fluctuations in heavy-ion collisions. Specifically we discuss a new Cooper-Frye particlization routine -- the subensemble sampler -- which is designed to incorporate effects of global conservation laws, thermal smearing and resonance decays on fluctuation measurements in various rapidity acceptances. First applications of the method to heavy-ion collisions at the LHC energies are presented and further necessary steps to analyze fluctuations from RHIC beam energy scan are outlined.

Measuring momentum-dependent flow fluctuations in heavy-ion collisions

In heavy-ion collisions, momentum-dependent pair correlations can be characterized by a principal component analysis (PCA), in which subleading modes are expected to reveal new information on flow fluctuations. However, we find that, as currently measured, these modes can be dominated by multiplicity fluctuations, which serve as an unwanted background. Here, we propose new PCA observables that are robust against multiplicity fluctuations and isolate novel sources of flow fluctuations, thus being suited to provide fresh insight into the initial stages of the system at small length scales.

Centrality Dependence of Multiplicity Fluctuations from a Hydrodynamical Approach

As one of the possible signals for the whereabouts of the critical point on the QCD phase diagram, recently, the multiplicity fluctuations in heavy-ion collisions have aroused much attention. It is a crucial observation of the Beam Energy Scan program of the Relativistic Heavy Ion Collider. In this work, we investigate the centrality dependence of the multiplicity fluctuations regarding the recent measurements from STAR Collaboration. By employing a hydrodynamical approach, the present study is dedicated to the noncritical aspects of the phenomenon. To be specific, in addition to the thermal fluctuations, finite volume corrections, and resonance decay at the freeze-out surface, the model is focused on the properties of the hydrodynamic expansion of the system and the event-by-event initial fluctuations. It is understood that the real signal of the critical point can only be obtained after appropriately subtracting the background; the latter is investigated in the present work. Besides the experimental data, our results are also compared to those of the hadronic resonance gas, as well as the transport models.

Hydrodynamic results on multiplicity fluctuations in heavy-ion collisions

Multiplicity fluctuations are one of the most crucial observables in the Beam Energy Scan program of the Relativistic Heavy Ion Collider. It is understood that they can be utilized to probe the whereabouts of the critical point on the phase diagram of the QCD matter. However, a significant portion of these fluctuations is, apart from that related to the QCD phase transition, attributed to the other origins, which we refer to as "noncritical" ones. The present study is dedicated to the noncritical aspects of the multiplicity fluctuations in heavy-ion collisions. In particular, we focus on those of dynamical origin, such as the hydrodynamic expansion of the system and the event-by-event initial fluctuations, in addition to the usual thermal fluctuations, finite volume corrections, and resonance decay at the freeze-out surface. The obtained results are compared to those of the hadronic resonance gas model as well as to the experimental data.