Hadron Resonance Gas Model Calculations Research Articles

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.

Collision-energy dependence of second-order off-diagonal and diagonal cumulants of net-charge, net-proton, and net-kaon multiplicity distributions in Au + Au collisions

We report the first measurements of a complete second-order cumulant matrix of net-charge, net-proton, and net-kaon multiplicity distributions for the first phase of the beam energy scan program at RHIC. This includes the centrality and, for the first time, the pseudorapidity window dependence of both diagonal and off-diagonal cumulants in Au+Au collisions at \sNN~= 7.7-200 GeV. Within the available acceptance of $|\eta|<0.5$, the cumulants grow linearly with the pseudorapidity window. Relative to the corresponding measurements in peripheral collisions, the ratio of off-diagonal over diagonal cumulants in central collisions indicates an excess correlation between net-charge and net-kaon, as well as between net-charge and net-proton. The strength of such excess correlation increases with the collision energy. The correlation between net-proton and net-kaon multiplicity distributions is observed to be negative at \sNN~= 200 GeV and change to positive at the lowest collision energy. Model calculations based on non-thermal (UrQMD) and thermal (HRG) production of hadrons cannot explain the data. These measurements will help map the QCD phase diagram, constrain hadron resonance gas model calculations, and provide new insights on the energy dependence of baryon-strangeness correlations. An erratum has been added to address the issue of self-correlation in the previously considered efficiency correction for off-diagonal cumulant measurement. Previously considered unidentified (net-)charge correlation results ($\sigma^{11}_{Q,p}$ and $\sigma^{11}_{Q,k})$ are now replaced with identified (net-)charge correlation ($\sigma^{11}_{Q^{PID},p}$ and $\sigma^{11}_{Q^{PID},k}$)

Conserved charge fluctuations at vanishing and non-vanishing chemical potential

Up to 6th order cumulants of fluctuations of net baryon-number, net electric charge and net strangeness as well as correlations among these conserved charge fluctuations are now being calculated in lattice QCD. These cumulants provide a wealth of information on the properties of strong-interaction matter in the transition region from the low temperature hadronic phase to the quark-gluon plasma phase. They can be used to quantify deviations from hadron resonance gas (HRG) model calculations which frequently are used to determine thermal conditions realized in heavy ion collision experiments. Already some second order cumulants like the correlations between net baryon-number and net strangeness or net electric charge differ significantly at temperatures above 155 MeV in QCD and HRG model calculations. We show that these differences increase at non-zero baryon chemical potential constraining the applicability range of HRG model calculations to even smaller values of the temperature.

QCD Thermodynamics in the Crossover/Freeze-out Region

We use results from a 6-th order Taylor expansion of the QCD equation of state to construct expansions for cumulants of conserved charge fluctuations and their correlations. We show that these cumulants strongly constrain the range of applicability of hadron resonance gas model calculations. We point out that the latter is inappropriate to describe equilibrium properties of QCD at zero and non-zero values of the baryon chemical potential already at T~155 MeV.

Lattice QCD results on cumulant ratios at freeze-out

Ratios of cumulants of net proton-number fluctuations measured by the STAR Collaboration show strong deviations from a skellam distribution, which should describe thermal properties of cumulant ratios, if proton-number fluctuations are generated in equilibrium and a hadron resonance gas (HRG) model would provide a suitable description of thermodynamics at the freeze-out temperature. We present some results on 6th order cumulants entering the calculation of the QCD equation of state at non-zero values of the baryon chemical potential (μB) and discuss limitations on the applicability of HRG thermodynamics deduced from a comparison between QCD and HRG model calculations of cumulants of conserved charge fluctuations. We show that basic features of the μB-dependence of skewness and kurtosis ratios of net proton-number fluctuations measured by the STAR Collaboration resemble those expected from a QCD calculation of the corresponding net baryon-number cumulant ratios.

Effect of resonance decay on conserved number fluctuations in a hadron resonance gas model

We study the effect of charged secondaries coming from resonance decay on the net-baryon, net-charge and net-strangeness fluctuations in high energy heavy-ion collisions within the hadron resonance gas (HRG) model. We emphasize the importance of including weak decays along with other resonance decays in the HRG, while comparing with the experimental observables. The effect of kinematic cuts on resonances and primordial particles on the conserved number fluctuations are also studied. The HRG model calculations with the inclusion of resonance decays and kinematical cuts are compared with the recent experimental data from STAR and PHENIX experiments. We find a good agreement between our model calculations and the experimental measurements for both net-proton and net-charge distributions.

Evidence for experimentally unobserved strange hadrons from QCD thermodynamics and their impact on freeze-out parameter

We analyze the influence of experimentally not yet observed strange hadrons – predicted by quark model calculations as well as lattice QCD – on QCD bulk thermodynamics. By comparing lattice QCD results of various combinations of net strangeness fluctuations to hadron resonance gas (HRG) model calculations with different strange hadron content, we find evidence for such additional hadronic states from QCD thermodynamics. We further investigate the impact of such states on the freeze-out parameter in heavy ion collisions. We show that the freeze-out temperature as determined from yields of strange baryons over anti-baryons is, in agreement with lattice QCD, lowered by 5–8 MeV in comparison with the conventional HRG model calculations.

Thermodynamics of Strong Interaction Matter from Lattice QCD and the Hadron Resonance Gas Model

We compare recent lattice QCD calculations of higher order cumulants of net-strangeness fluctuations with hadron resonance gas (HRG) model calculations. Up to the QCD transition temperature Tc = (154 ± 9) MeV we find good agreement between QCD and HRG model calculations of second and fourth order cumulants, even when subtle aspects of net-baryon number, strangeness and electric charge fluctuations are probed. In particular, the fourth order cumulants indicate that also in the strangeness sector of QCD the failure of HRG model calculations sets in quite abruptly in the vicinity of the QCD transition temperature and is apparent in most observables for T ≳ 160 MeV.

Higher Moments of the Net-charge Multiplicity Distributions at RHIC Energies in STAR

We report the higher order moments of the net-charge multiplicity distributions for the Au+Au collisions at \sNN = 7.7, 11.5, 19.6, 27, 39, 62.4 and 200 GeV in the STAR experiment at the Relativistic Heavy-Ion Collider (RHIC). The energy and centrality dependence of higher moments and their products (such as $\sigma^2/M$, $S\sigma$ and $\kappa\sigma^{2}$) are presented. The data are also compared to Poisson expectations and Hadron Resonance Gas model calculations.

Fluctuations and correlations of net baryon number, electric charge, and strangeness: A comparison of lattice QCD results with the hadron resonance gas model

We calculate the quadratic fluctuations of net baryon number, electric charge and strangeness as well as correlations among these conserved charges in ($2+1$)-flavor lattice QCD at zero chemical potential. Results are obtained using calculations with tree-level improved gauge and the highly improved staggered quark actions with almost physical light and strange quark masses at three different values of the lattice cutoff. Our choice of parameters corresponds to a value of 160 MeV for the lightest pseudoscalar Goldstone mass and a physical value of the kaon mass. The three diagonal charge susceptibilities and the correlations among conserved charges have been extrapolated to the continuum limit in the temperature interval $150\text{ }\text{ }\mathrm{MeV}\ensuremath{\le}T\ensuremath{\le}250\text{ }\text{ }\mathrm{MeV}$. We compare our results with the hadron resonance gas (HRG) model calculations and find agreement with HRG model results only for temperatures $T\ensuremath{\lesssim}150\text{ }\text{ }\mathrm{MeV}$. We observe significant deviations in the temperature range $160\text{ }\text{ }\mathrm{MeV}\ensuremath{\lesssim}T\ensuremath{\lesssim}170\text{ }\text{ }\mathrm{MeV}$ and qualitative differences in the behavior of the three conserved charge sectors. At $T\ensuremath{\simeq}160\text{ }\text{ }\mathrm{MeV}$ quadratic net baryon number fluctuations in QCD agree with HRG model calculations, while the net electric charge fluctuations in QCD are about 10% smaller and net strangeness fluctuations are about 20% larger. These findings are relevant to the discussion of freeze-out conditions in relativistic heavy ion collisions.

Hadron mass spectrum and the shear viscosity to entropy density ratio of hot hadronic matter

Lattice calculations of the QCD trace anomaly at temperatures $T<160$ MeV have been shown to match hadron resonance gas model calculations, which include an exponentially rising hadron mass spectrum. In this paper we perform a more detailed comparison of the model calculations to lattice data that confirms the need for an exponentially increasing density of hadronic states. Also, we find that the lattice data is compatible with a hadron density of states that goes as $\rho(m) \sim m^{-a}\exp(m/T_H) $ at large $m$ with $a> 5/2$ (where $T_H \sim 167$ MeV). With this specific subleading contribution to the density of states, heavy resonances are most likely undergo 2-body decay (instead of multi-particle decay), which facilitates their inclusion into hadron transport codes. Moreover, estimates for the shear viscosity and the shear relaxation time coefficient of the hadron resonance model computed within the excluded volume approximation suggest that these transport coefficients are sensitive to the parameters that define the hadron mass spectrum.

Search for the QCD Critical Point by Higher Moments of Net-proton Multiplicity Distributions at RHIC

Higher moments of net-proton multiplicity distributions are applied to search for the QCD critical point. In this paper, we will present measurements for kurtosis ($\kappa$), skewness ($S$) and variance $\sigma^2$) of net-proton multiplicity distributions at the mid-rapidity ($|y|<0.5$) and transverse momentum range $0.4<p_{T}<0.8$ {\gevc} for Au+Au collisions at {\sNN} = 7.7, 11.5, 39, 62.4 and 200 GeV, Cu+Cu collisions at {\sNN} = 22.4, 62.4 and 200 GeV, $d$+Au collisions at {\sNN} = 200 GeV and p+p collisions at {\sNN} = 62.4 and 200 GeV. The moment products $\kappa \sigma^2$ and $S \sigma$ of net-proton distributions, which are related to volume independent baryon number susceptibility ratios, are consistent with Lattice QCD and Hadron Resonance Gas (HRG) model calculations at high energies ({\sNN} = 62.4 and 200 GeV). Deviations of $\kappa \sigma^2$ and $S\sigma$ for the Au+Au collisions at low energies ({\sNN} = 7.7, 11.5 and 39 GeV) from HRG model calculations are also observed.

Probing the QCD Critical Point with Higher Moments of Net-proton Multiplicity Distributions

Higher moments of event-by-event net-proton multiplicity distributions are applied to search for the QCD critical point in the heavy ion collisions. It has been demonstrated that higher moments as well as moment products are sensitive to the correlation length and directly connected to the thermodynamic susceptibilities computed in the Lattice QCD and Hadron Resonance Gas (HRG) model. In this paper, we will present measurements for kurtosis (k), skewness (S) and variance (σ2) of net-proton multiplicity distributions at the mid-rapidity (|y| < 0.5) and 0.4 < pT < 0.8 GeV/c for Au+Au collisions at = 19.6, 39, 62.4, 130 and 200 GeV, Cu+Cu collisions at = 22.4, 62.4 and 200 GeV, d+Au collisions at = 200 GeV and p+p collisions at = 62.4 and 200 GeV. The moment products kσ2 and Sσ of net-proton distributions, which are related to volume independent baryon number susceptibility ratio, are compared to the Lattice QCD and HRG model calculations. The kσ2 and Sσ of net-proton distributions are consistent with Lattice QCD and HRG model calculations at high energy, which support the thermalization of the colliding system. Deviations of kσ2 and Sσ for the Au+Au collisions at low energies from HRG model calculations are also observed.

Probing freeze-out conditions in heavy ion collisions with moments of charge fluctuations

We calculate the first four moments of baryon number, electric charge and strangeness fluctuations within the hadron resonance gas model. Different moments and their ratios as well as skewness and kurtosis are evaluated on the phenomenologically determined freeze-out curve in the temperature, baryon chemical potential plane. The model results and its predictions as well as relations between different moments are compared with the first data on net proton fluctuations in Au–Au collisions obtained at RHIC by the STAR Collaboration. We find good agreement between the model calculations and experimental results. We also point out that higher order moments should be more sensitive to critical behavior and will also distinguish hadron resonance gas model calculations from results obtained from lattice QCD.

QCD phase diagram: A comparison of lattice and hadron resonance gas model calculations

We compare the lattice results on QCD phase diagram for two and three flavors with the hadron resonance gas model (HRGM) calculations. Lines of constant energy density $ϵ$ have been determined at different baryo-chemical potentials ${\ensuremath{\mu}}_{B}$. For the strangeness chemical potentials ${\ensuremath{\mu}}_{S}$, we use two models. In one model, we explicitly set ${\ensuremath{\mu}}_{S}=0$ for all temperatures and baryo-chemical potentials. This assignment is used in lattice calculations. In the other model, ${\ensuremath{\mu}}_{S}$ is calculated in dependence on $T$ and ${\ensuremath{\mu}}_{B}$ according to the condition of vanishing strangeness. We also derive an analytical expression for the dependence of ${T}_{c}$ on ${\ensuremath{\mu}}_{B}/T$ by applying Taylor expansion of $ϵ$. In both cases, we compare HRGM results on ${T}_{c}\ensuremath{-}{\ensuremath{\mu}}_{B}$ diagram with the lattice calculations. The agreement is excellent, especially when the trigonometric function of $ϵ$ is truncated up to the same order as done in lattice simulations. For studying the efficiency of the truncated Taylor expansion, we calculate the radius of convergence. For zero- and second-order radii, the agreement with lattice is convincing. Furthermore, we make predictions for QCD phase diagram for nontruncated expressions and physical masses. These predictions are to be confirmed by heavy-ion experiments and future lattice calculations with very small lattice spacing and physical quark masses.

Thermodynamics at non-zero baryon number density: a comparison of lattice and hadron resonance gas model calculations

We compare recent lattice studies of QCD thermodynamics at non-zero quark chemical potential with the thermodynamics of a hadron resonance gas. We argue that for T⩽Tc the equation of state derived from Monte Carlo simulations of two flavour QCD at non-zero chemical potential can be well described by a hadron resonance gas when using the same set of approximations as used in current lattice calculations. We estimate the importance of truncation errors arising from the use of a Taylor expansion in terms of the quark chemical potential and examine the influence of unphysically large quark masses on the equation of state and the critical conditions for deconfinement.