Hadron Resonance Gas Research Articles

Modified equilibrium distributions for Cooper-Frye particlization

We introduce a positive definite single-particle distribution that is suitable for describing the transition from a macroscopic hydrodynamic to a microscopic kinetic description during the late stages of heavy-ion collisions in the presence of moderately large viscous corrections. The modified equilibrium distribution function can be constructed with hydrodynamic input from either relativistic viscous fluid dynamics or anisotropic fluid dynamics. We test the modified equilibrium distribution's hydrodynamic output for a stationary hadron resonance gas subject to either shear stress, bulk pressure, or baryon diffusion current at a given freeze-out temperature and baryon chemical potential. While it does not reproduce all components of the net baryon current and energy-momentum tensor exactly, it significantly improves upon the customary linearized approximations for the non-equilibrium correction $\delta f_n$ which typically lead to unphysical negative distribution functions at large particle momenta. A comparison of particle spectra and $p_T$-differential elliptic flow coefficients from the Cooper-Frye formula computed with the modified equilibrium distribution and with linearized $\delta f_n$ corrections is presented, for two different (2+1)-dimensional hypersurfaces corresponding to central and non-central Pb+Pb collisions at the Large Hadron Collider (LHC).

Fluctuations and correlations of net baryon number, electric charge and strangeness in a background magnetic field

We present results on the second-order fluctuations of and correlations among net baryon number, electric charge and strangeness in (2+1)-flavor lattice QCD in the presence of a background magnetic field. Simulations are performed using the tree-level improved gauge action and the highly improved staggered quark (HISQ) action with a fixed scale approach ($a\simeq$ 0.117 fm). The light quark mass is set to be 1/10 of the physical strange quark mass and the corresponding pion mass is about 220 MeV at vanishing magnetic field. Simulations are performed on $32^3\times N_\tau$ lattices with 9 values of $N_\tau$ varying from 96 to 6 corresponding to temperatures ranging from zero up to 281 MeV. The magnetic field strength $eB$ is simulated with 15 different values up to $\sim$2.5 GeV$^2$ at each nonzero temperature. We find that quadratic fluctuations and correlations do not show any singular behavior at zero temperature in the current window of $eB$ while they develop peaked structures at nonzero temperatures as $eB$ grows. By comparing the electric charge-related fluctuations and correlations with hadron resonance gas model calculations and ideal gas limits we find that the changes in degrees of freedom start at lower temperatures in stronger magnetic fields. Significant effects induced by magnetic fields on the isospin symmetry and ratios of net baryon number and baryon-strangeness correlation to strangeness fluctuation are observed, which could be useful for probing the existence of a magnetic field in heavy-ion collision experiments.

An Approach of Statistical Corrections to Interactions in Hadron Resonance Gas

We propose a new model for hadrons with quantum mechanical attractive and repulsive interactions sensitive to some spatial correlation length parameter inspired by the Beth-Uhlenbeck quantum mechanical nonideal gas model (Uhlenbeck and Beth, 1937). We confront the thermodynamics calculated using our model with a corresponding recent lattice data at four different values of the baryon chemical potential, μ b = 0 , 170 , 340 , 425 MeV over temperatures ranging from 130 MeV to 200 MeV and for five values for the correlation length ranging from 0 to 0.2 fm. For equilibrium temperatures up to the vicinity of the chiral phase transition temperature ≃160 MeV, a decent fitting between the model and the lattice data is observed for different values of r , especially at μ b , r = 170 , 0.05 , 340 , 0.1 , and 340 , 0.15 , where μ b is in MeV and r is in fm. For the vanishing chemical potential, the uncorrelated model r = 0 , which corresponds to the ideal hadron resonance gas model, seems to offer the best fit. The quantum hadron correlations seem to be more probable at nonvanishing chemical potentials, especially within the range μ b ∈ 170 , 340 MeV .

Centrality Dependence of Chemical Freeze-Out Parameters and Strangeness Equilibration in RHIC and LHC Energies

We have estimated centrality variation of chemical freeze-out parameters from yield data at midrapidity of π ± , K ± and p , p ¯ for collision energies of RHIC (Relativistic Heavy Ion Collider), Beam Energy Scan (RHIC-BES) program, and LHC (Large Hadron Collider). We have considered a simple hadron resonance gas model and employed a formalism involving conserved charges ( B , Q , S ) of QCD for parameterization. Along with temperature and three chemical potentials ( T , μ B , μ Q , μ S ), a strangeness undersaturation factor ( γ S ) has been used to incorporate the partial equilibration in the strange sector. Our obtained freeze-out temperature does not vary much with centrality, whereas chemical potentials and γ S seem to have a significant dependence. The strange hadrons are found to deviate from a complete chemical equilibrium at freeze-out at the peripheral collisions. This deviation appears to be more prominent as the collision energy decreases at lower RHIC-BES energies. We have also shown that this departure from equilibrium reduces towards central collisions, and strange particle equilibration may happen after a threshold number of participants in A - A collision.

Thermoelectric transport coefficients of hot and dense QCD matter

The presence of a nonvanishing thermal gradient and/or a chemical potential gradient in a conducting medium can lead to an electric field—an effect known as thermoelectric effect or Seebeck effect. We discuss here the thermoelectric effects for hot and dense strongly interacting matter within the framework of relativistic Boltzmann equation in the relaxation time approximation. In the context of heavy-ion collisions, the Seebeck coefficients for the quark matter as well as for the hadronic matter are estimated within this approach. The quark matter is modeled by the two flavor Nambu–Jona–Lassinio (NJL) model and the hadronic medium is modeled by the hadron resonance gas (HRG) model with hadrons and their resonances up to a mass cutoff $${\tilde{\varLambda }}\sim 2.6$$ GeV. For the estimation of thermoelectric transport coefficients, for the quark matter, we calculate the relaxation times for the quarks and antiquarks from the quark–quark and quark–antiquark scattering through meson exchange within the NJL model. On the other hand, for the hadronic medium, the relaxation times of hadrons and their resonances are estimated within a hard sphere scattering approximation. We also discuss the formalism of the thermoelectric effect in the presence of a nonvanishing external magnetic field. We give an estimation of the associated magneto-Seebeck coefficient and the Nernst coefficient for the hot and dense QCD matter.

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.

Quark Cluster Expansion Model for Interpreting Finite-T Lattice QCD Thermodynamics

In this work, we present a unified approach to the thermodynamics of hadron–quark–gluon matter at finite temperatures on the basis of a quark cluster expansion in the form of a generalized Beth–Uhlenbeck approach with a generic ansatz for the hadronic phase shifts that fulfills the Levinson theorem. The change in the composition of the system from a hadron resonance gas to a quark–gluon plasma takes place in the narrow temperature interval of 150–190 MeV, where the Mott dissociation of hadrons is triggered by the dropping quark mass as a result of the restoration of chiral symmetry. The deconfinement of quark and gluon degrees of freedom is regulated by the Polyakov loop variable that signals the breaking of the Z(3) center symmetry of the color SU(3) group of QCD. We suggest a Polyakov-loop quark–gluon plasma model with O(αs) virial correction and solve the stationarity condition of the thermodynamic potential (gap equation) for the Polyakov loop. The resulting pressure is in excellent agreement with lattice QCD simulations up to high temperatures.

Effects of hadronic repulsive interactions on the fluctuations of conserved charges

We investigate the effects of repulsive interaction between hadrons on the fluctuations of the conserved charges. We calculate the baryon,the electric charge and the strangeness susceptibilities within the ambit of hadron resonance gas model extended to include the short range repulsive interactions.The repulsive interactions are included through a mean-field approach where the single particle energy gets modified due to mean field interactions between hadrons proportional to the number density of hadrons.We assume different mean-field interactions for mesons and baryons. It is shown that the repulsive interactions play a very crucial role to describe hadronic matter near transition temperature. We also show that in order to consistently describe higher order conserved charge fluctuations mesonic repulsive interactions cannot be neglected. Further, we demonstrate that the repulsive interaction of baryons are essential to describe the lattice simulation results at finite baryonchemical potential for higher order fluctuations.

QCD equation of state at finite chemical potentials for relativistic nuclear collisions

We review the equation of state of QCD matter at finite densities. We discuss the construction of the equation of state with net baryon number, electric charge, and strangeness using the results of lattice QCD simulations and hadron resonance gas models. Its application to the hydrodynamic analyses of relativistic nuclear collisions suggests that the interplay of multiple conserved charges is important in the quantitative understanding of the dense nuclear matter created at lower beam energies. Several different models of the QCD equation of state are discussed for comparison.

Modified excluded volume hadron resonance gas model with Lorentz contraction

In this work we discuss a modified version of Excluded Volume Hadron Resonance Gas model and also study the effect of Lorentz contraction of the excluded volume on scaled pressure and susceptibilities of conserved charges. We find that the Lorentz contraction, coupled with the variety of excluded volume parameters reproduces the lattice QCD data quite satisfactorily.

Deconfining phase boundary of rapidly rotating hot and dense matter and analysis of moment of inertia

We discuss the effect of rapid rotation on the phase diagram of hadronic matter. The energy dispersion relation is shifted by an effective chemical potential induced by rotation. This suggests that rotation should lower the critical temperature of chiral restoration, but it is still controversial how the deconfinement temperature should change as a function of angular velocity. We adopt the hadron resonance gas model as an approach free from fitting parameters. We identify the deconfinement from the thermodynamic behavior and find that rotation decreases the deconfinement temperature. We also discuss the spatial inhomogeneity of the pressure and give a semi-quantitative estimate of the moment of inertia.

Resolving the hyper-triton yield description puzzle in high energy nuclear collisions

The recently developed hadron resonance gas model with multicomponent hard-core repulsion is used to address and resolve the long standing problem to describe the light nuclear cluster multiplicities including the hyper-triton measured by the STAR Collaboration, known as the hyper-triton chemical freeze-out puzzle. An improved description for the hadronic and light nuclear cluster data measured by STAR at the collision energy sqrt{s_{NN}} =200 GeV and by ALICE at sqrt{s_{NN}} =2.76 TeV is obtained. This is achieved by applying a new strategy of analyzing the light nuclear cluster data and by using the value for the hard-core radius of the (anti-)varLambda hyperons found in earlier work. One of the most striking results of the present work is that for the most probable scenario of chemical freeze-out for the STAR energy the obtained parameters allow to simultaneously reproduce the values of the experimental ratios S_3 and {overline{S}}_3 which were not included in the fit.

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.

Flavour and energy dependence of chemical freeze-out temperatures in relativistic heavy ion collisions from RHIC-BES to LHC energies

We present calculations of the chemical freeze-out temperature (Tch) based on particle yields from STAR and ALICE measured at collision energies ranging from sNN= 11.5 GeV to 5.02 TeV. Employing the Grand Canonical Ensemble approach using the Thermal-FIST Hadron Resonance Gas model package, we show evidence for a flavour-dependent chemical freeze-out in the crossover region of the QCD phase diagram. At a vanishing baryochemical potential, we calculate light and strange flavour freeze-out temperatures TL=150.2±2.6 MeV and TS=165.1±2.7 MeV, respectively.

Multiplicity dependence of (multi)strange baryons in the canonical ensemble with phase shift corrections

The increase in strangeness production with charged particle multiplicity, as seen by the ALICE collaboration at CERN in $p\text{\ensuremath{-}}p$, $p$-Pb, and Pb-Pb collisions, is investigated in the hadron resonance gas model taking into account interactions among hadrons using $S$-matrix corrections based on known phase shift analyses. Strangeness conservation is taken into account in the framework of the canonical strangeness ensemble. A very good description is obtained for the variation of the strangeness content in the final state as a function of the number of charged hadrons in the midrapidity region using the same fixed temperature value as obtained in the most central Pb-Pb collisions and with a fixed strangeness suppression factor ${\ensuremath{\gamma}}_{s}=1$. It is shown that the number of charged hadrons is linearly proportional to the volume of the system. For small multiplicities the canonical ensemble with local strangeness conservation restricted to midrapidity leads to a stronger suppression of (multi)strange baryons than seen in the data. This is compensated by introducing a global conservation of strangeness in the whole phase-space which is parametrized by the canonical correlation volume larger than the fireball volume at the midrapidity. The results on comparing the hadron resonance gas model with and without S-matrix corrections, are presented in detail. It is shown that the interactions introduced by the phase shift analysis via the $S$-matrix formalism are essential for a better description of the yields data.

Pion Condensation in the Early Universe at Nonvanishing Lepton Flavor Asymmetry and Its Gravitational Wave Signatures.

We investigate the possible formation of a Bose-Einstein condensed phase of pions in the early Universe at nonvanishing values of lepton flavor asymmetries. A hadron resonance gas model with pion interactions, based on first-principle lattice QCD simulations at nonzero isospin density, is used to evaluate cosmic trajectories at various values of electron, muon, and tau lepton asymmetries that satisfy the available constraints on the total lepton asymmetry. The cosmic trajectory can pass through the pion condensed phase if the combined electron and muon asymmetry is sufficiently large: |l_{e}+l_{μ}|≳0.1, with little sensitivity to the difference l_{e}-l_{μ} between the individual flavor asymmetries. Future constraints on the values of the individual lepton flavor asymmetries will thus be able to either confirm or rule out the condensation of pions during the cosmic QCD epoch. We demonstrate that the pion condensed phase leaves an imprint both on the spectrum of primordial gravitational waves and on the mass distribution of primordial black holes at the QCD scale, e.g., the black hole binary of recent LIGO event GW190521 can be formed in that phase.

Deconfinement and Hadron Resonance Gas for Heavy Quarks

I discuss the deconfinement transition in 2+1 flavor QCD in terms of Polyakov loops as well as the hadron resonance gas for hadrons containing static quarks and charm quarks.

Hadronic Resonance Gas Model and Multiplicity Dependence in \(p\)–\(p\), \(p\)–Pb, Pb–Pb Collisions: Strangeness Enhancement

Recently the ALICE collaboration has observed an interesting systematic behaviour of ratios of identified particles to pions yields at the LHC, showing that they depend solely on the charged-particle multiplicity in pp, pPb and PbPb collisions. In particular, the yields of (multi)strange particles relative to pions, increases with multiplicity and the enhancement is mode pronounced with increasing strangeness content. We will argue, that such a pattern of arises naturally in the thermal model taking into account exact strangeness conservation. Furthermore, extending the thermal model by including hadron interactions within the S-matrix approach, the ALICE data can be well quantified by the thermal particle yields at the chiral-crossover temperature, as previously found in central Pb-Pb collisions.

Chemical freeze-out parameters of net-kaons in heavy-ion collisions

We study chemical freeze-out parameters for heavy-ion collisions by performing two different thermal analyses. We analyze results from thermal fits for particle yields, as well as, net-charge fluctuations in order to characterize the chemical freeze-out. The Hadron Resonance Gas (HRG) model is employed for both methods. By separating the light hadrons from the strange hadrons in thermal fits, we study the proposed flavor hierarchy. For the net-charge fluctuations, we calculate the mean-over-variance ratio of the net-kaon fluctuations in the HRG model at the five highest energies of the RHIC Beam Energy Scan (BES) for different particle data lists. We compare these results with recent experimental data from the STAR collaboration in order to extract sets of chemical freeze-out parameters for each list. We focused on particle lists which differ largely in the number of resonant states. By doing so, our analysis determines the effect of the amount of resonances included in the HRG model on the freeze-out conditions. Our findings have potential impact on various other models in the field of relativistic heavy ion collisions.

Recent results on conserved charge fluctuations in ALICE

Recent results on the analysis of event-by-event net-baryon number fluctuations in Pb–Pb collisions at sNN=2.76 and 5.02 TeV are presented. The cumulants of the net-proton distributions, proxies for the net-baryon distributions, up to third order are discussed. The experimental results are compared with HIJING and EPOS model calculations and the dependence of fluctuation measurements on the phase-space coverage is addressed in the context of calculations from Lattice QCD (LQCD) and the Hadron Resonance Gas (HRG) model.