Net-proton Number Fluctuations Research Articles

Experimental search for the QCD critical endpoint

The phase diagram of strong interaction has been a subject of intense theoretical and experimental research. One of the big questions in this regard is whether a critical endpoint is associated with the phase transition of strongly interacting matter. There have been rapid theoretical developments to answer this question. On the experimental side, a tremendous effort is put forward to hunt for the critical point in collisions of atomic nuclei. This article gives an experimental overview of some of the key results for critical point searches, mainly focusing on net-proton number fluctuations in nuclear collisions.

First Measurement of Antideuteron Number Fluctuations at Energies Available at the Large Hadron Collider.

The first measurement of event-by-event antideuteron number fluctuations in high energy heavy-ion collisions is presented. The measurements are carried out at midrapidity (|η|<0.8) as a function of collision centrality in Pb-Pb collisions at sqrt[s_{NN}]=5.02 TeV using the ALICE detector. A significant negative correlation between the produced antiprotons and antideuterons is observed in all collision centralities. The results are compared with a state-of-the-art coalescence calculation. While it describes the ratio of higher order cumulants of the antideuteron multiplicity distribution, it fails to describe quantitatively the magnitude of the correlation between antiproton and antideuteron production. On the other hand, thermal-statistical model calculations describe all the measured observables within uncertainties only for correlation volumes that are different with respect to those describing proton yields and a similar measurement of net-proton number fluctuations.

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.

Beam Energy Dependence of Fifth- and Sixth-Order Net-Proton Number Fluctuations in Au+Au Collisions at RHIC

We report the beam energy and collision centrality dependence of fifth and sixth order cumulants (C_{5}, C_{6}) and factorial cumulants (κ_{5}, κ_{6}) of net-proton and proton number distributions, from center-of-mass energy (sqrt[s_{NN}]) 3GeV to 200GeV Au+Au collisions at RHIC. Cumulant ratios of net-proton (taken as proxy for net-baryon) distributions generally follow the hierarchy expected from QCD thermodynamics, except for the case of collisions at 3GeV. The measured values of C_{6}/C_{2} for 0%-40% centrality collisions show progressively negative trend with decreasing energy, while it is positive for the lowest energy studied. These observed negative signs are consistent with QCD calculations (for baryon chemical potential, μ_{B}≤110 MeV) which contains the crossover transition range. In addition, for energies above 7.7GeV, the measured proton κ_{n}, within uncertainties, does not support the two-component (Poisson+binomial) shape of proton number distributions that would be expected from a first-order phase transition. Taken in combination, the hyperorder proton number fluctuations suggest that the structure of QCD matter at high baryon density, μ_{B}∼750 MeV at sqrt[s_{NN}]=3 GeV is starkly different from those at vanishing μ_{B}∼24 MeV at sqrt[s_{NN}]=200 GeV and higher collision energies.

Deciphering the phases of QCD matter with fluctuations and correlations of conserved charges

A review is given on recent experimental and theoretical/phenomenological developments regarding the phase structure of the strongly interacting matter. Specifically, evolution with collision energy of netproton number fluctuations as measured by several experiments are presented and their implications for the QCD phase diagram are outlined. In addition, theoretical calculations on correlations between conserved charges are presented and prospects for their experimental explorations are addressed.

Net-proton number cumulant ratios as a function of beam energy from an expanding nonequilibrium chiral fluid

The beam energy scan program at RHIC provides data on net-proton number fluctuations with the goal to detect the QCD critical end point and first-order phase transition. Interpreting these experimental signals requires a vital understanding of the interplay of critical phenomena and the nonequilibrium dynamics of the rapidly expanding fireball. We study these aspects with a fluid dynamic expansion coupled to the explicit propagation of the chiral order parameter sigma via a Langevin equation. Assuming a sigma-proton coupling through an effective proton mass, we relate cumulants of the order parameter and the net-proton number at freeze-out and obtain observable cumulant ratios as a function of beam energy. We emphasize the role of the nonequilibrium first-order phase transition where a mixed phase with gradual freeze-out can significantly alter the cumulants. We find that the presence of a critical end point is clearly visible in the cumulant ratios for a relatively wide range of center-of-mass energies.

QCD Critical Point and Net-Proton Number Fluctuations at RHIC-STAR

In the search of QCD phase boundary and critical point, higher-order cumulants of conserved quantities are proposed as promising observables and have been studied extensively both experimentally and theoretically. In this paper we present cumulant ratios up to 6th-order of net-proton number distributions in Au+Au collisions at √SNN = 7.7 - 200 GeV from STAR Beam Energy Scan program phase I and √S = 200 GeV p + p collisions. The results are compared with various models and Lattice QCD calculations.

Net-proton number fluctuations and the Quantum Chromodynamics critical point: Supplemental material

Net-proton number fluctuations and the Quantum Chromodynamics critical point: Supplemental material

Relativistic nuclear collisions: Establishing a non-critical baseline for fluctuation measurements

We study the influence of global baryon number conservation on the non-critical baseline of net baryon cumulants in heavy-ion collisions in a given acceptance, accounting for the asymmetry between the mean-numbers of baryons and antibaryons. We derive the probability distribution of net baryon number in a restricted phase space from the canonical partition function that incorporates exact conservation of baryon number in the full system. Furthermore, we provide tools to compute cumulants of any order from the generating function of uncorrelated baryons constrained by exact baryon number conservation. The results are applied to quantify the non-critical baseline for cumulants of net proton number fluctuations obtained in heavy-ion collisions by the STAR collaboration at different RHIC energies and by the ALICE collaboration at the LHC. Furthermore, volume fluctuations are added by a Monte Carlo procedure based on the centrality dependence of charged particle production as measured experimentally. Compared to the predictions based on the hadron resonance gas model or Skellam distribution a clear suppression of fluctuations is observed due to exact baryon-number conservation. The suppression increases with the order of the cumulant and towards lower collision energies. Predictions for net proton cumulants up to the eight order in heavy-ion collisions are given for experimentally accessible collision energies.

Baseline study for net-proton number fluctuations at top energies available at the BNL Relativistic Heavy Ion Collider and at the CERN Large Hadron Collider with the Angantyr model

The multiplicity percentile dependence of cumulants, of net-proton number distributions in Au$-$Au collisions at $\sqrt{s_{NN}} = $ 200 GeV and Pb$-$Pb collisions at $\sqrt{s_{NN}} = $ 2.76 TeV has been investigated using the Angantyr model (the heavy-ion extension of the \textsc{Pythia 8} model). The effects of finite transverse momentum ($p_{\mathrm T}$) and pseudorapidity ($\eta$) acceptance on the net-proton cumulants have also been studied. Furthermore, the effects of the hydrodynamic expansion and feed down from weak decays were explored. It was found that radial flow has substantial impact on the cumulants and their ratios, while weak decays have a finite but relatively smaller effect. The obtained values of cumulants and their ratios with the Angantyr model, where the formation of thermalized medium is not assumed can serve as a baseline for future measurements.

Net-proton number fluctuations in the presence of the QCD critical point

Event-by-event fluctuations of the net-proton number studied in heavy-ion collisions provide an important means in the search for the conjectured critical end point (CP) in the QCD phase diagram. We propose a phenomenological model in which the fluctuations of the chiral critical mode couple to protons and anti-protons. This allows us to study the behavior of the net-proton number fluctuations in the presence of the CP. Calculating the net-proton number cumulants, Cn with n = 1, 2, 3, 4, along the phenomenological freeze-out line we show that the ratio of variance and mean C2/C1, as well as kurtosis C4/C2 resemble qualitative properties observed in data in heavy-ion collisions as a function of beam energy obtained by the STAR Collaboration at RHIC. In particular, the non-monotonic structure of the kurtosis and smooth change of the C2/C1 ratio with beam energy could be due to the CP located near the freeze-out line. The skewness, however, exhibits properties that are in contrast to the criticality expected due to the CP. The dependence of our results on the model parameters and the proximity of the chemical freeze-out to the critical point are also discussed.

Searching for the QCD Critical Point with Net-Proton Number Fluctuations

Net-proton number fluctuations can be measured experimentally and, hence, provide a source of important information about the matter created during relativistic heavy ion collisions. Particularly, they may give us clues about the conjectured QCD critical point. In this work, the beam-energy dependence of ratios of the first four cumulants of the net-proton number is discussed. These quantities are calculated using a phenomenologically motivated model in which critical mode fluctuations couple to protons and antiprotons. Our model qualitatively captures both the monotonic behavior of the lowest-order ratio, as well as the non-monotonic behavior of higher-order ratios, as seen in the experimental data from the STAR Collaboration. We also discuss the dependence of our results on the coupling strength and the location of the critical point.

Nuclear interactions and net-proton number fluctuations in heavy ion collisions at the SIS18 accelerator

The effect of nuclear interactions on measurable net-proton number fluctuations in heavy ion collisions at the SIS18/GSI accelerator is investigated. The state of the art UrQMD model including interaction potentials is employed. It is found that the nuclear forces enhance the baryon number cumulants, as predicted from grand canonical thermodynamical models. The effect however is smeared out for proton number fluctuations due to iso-spin randomization and global baryon number conservation, which decreases the cumulant ratios. For a rapidity acceptance window larger than Δy>0.4 the effects of global baryon number conservation dominate and all cumulant ratios are significantly smaller than 1.

Critical point of nuclear matter and beam-energy dependence of net-proton number fluctuations

The beam energy dependence of net baryon number susceptibilities is studied in the framework of the hadron resonance gas model with the attractive and repulsive van der Waals interactions between baryons. The collision energy dependences for the skewness $S\sigma$ and kurtosis $\kappa\sigma^2$ deviate significantly from the Poisson baseline and demonstrate the existence of rich structures at moderate collision energies. This behavior may result from the critical end point of the nuclear liquid-gas first order phase transition. In particular, $\kappa\sigma^2$ shows a non-monotonic energy dependence, and, in contrast to the standard scenario for the QCD critical point, it does not decrease at low collision energies. It is also found that the measurable net proton fluctuations differ significantly from the net baryon fluctuations when interactions between baryons cannot be neglected. The results are compared with the experimental net proton number fluctuations measured by the STAR collaboration.

Overview of recent results from HADES

HADES is a multi-purpose charged-particle detector operated at the SIS18 synchrotron located at the GSI Helmholtz Center for Heavy Ion Research in Darmstadt, Germany. The provided ion beam energies of 1-2 A GeV are the lowest of all currently running heavy-ion experiments and result in the highest baryo-chemical potentials at freeze-out in case of Au+Au collisions. At this Quark Matter conference we presented results from Au+Au collisions at sNN=2.4GeV. The created system exhibits a very clear hierarchy in hadron yields, with about 100 protons, 10 pions, 10−2 kaons and 10−4 antikaons per event. The HADES program focuses on four main observables: (subthreshold) strangeness production, particle flow and its anisotropies, virtual photon emission and net-proton number fluctuations.

Conserved Charge Fluctuations from Lattice QCD and the Beam Energy Scan

We discuss the next-to-leading order Taylor expansion of ratios of cumulants of net-baryon number fluctuations. We focus on the relation between the skewness ratio, SBσB≡χ3B/χ1B, and the kurtosis ratio, κBσB2≡χ4B/χ2B. We show that differences in these two cumulant ratios are small for small values of the baryon chemical potential. The next-to-leading order correction to κBσB2 however is approximately three times larger than that for SBσB. The former thus drops much more rapidly with increasing beam energy, sNN. We argue that these generic patterns are consistent with current data on cumulants of net-proton number fluctuations measured by the STAR Collaboration at sNN≥19.6 GeV.

Probing the QCD chiral cross-over transition in heavy ion collisions

Abstract We argue that by measuring higher moments of the net proton number fluctuations in heavy ion collisions (HIC) one can probe the QCD chiral cross-over transition experimentally. We discuss the properties of fluctuations of the net baryon number in the vicinity of the chiral cross-over transition within the Polyakov loop extended quark-meson model at finite temperature and baryon density. The calculation includes non-perturbative dynamics implemented within the functional renormalization group approach. We find a clear signal for the chiral cross-over transition in the fluctuations of the net baryon number. We address our theoretical findings to experimental data of the STAR Collaboration on energy and centrality dependence of the net proton number fluctuations and their probability distributions in HIC.

Fluctuations as probe of the QCD phase transition and freeze-out in heavy ion collisions at LHC and RHIC

We discuss the relevance of higher order moments of net baryon number fluctuations for the analysis of freeze-out and critical conditions in heavy ion collisions at LHC and RHIC. Using properties of O(4) scaling functions, we discuss the generic structure of these higher moments at vanishing baryon chemical potential and apply chiral model calculations to explore their properties at non-zero baryon chemical potential. We show that the ratios of the sixth to second and eighth to second order moments of the net baryon number fluctuations change rapidly in the transition region of the QCD phase diagram. Already at vanishing baryon chemical potential they deviate considerably from the predictions of the hadron resonance gas model which reproduce the second to fourth order moments of the net proton number fluctuations at RHIC. We point out that the sixth order moments of baryon number and electric charge fluctuations remain negative at the chiral transition temperature. Thus, they offer the possibility to probe the proximity of the thermal freeze-out to the crossover line.