Hagedorn states are the key to understand how all hadrons observed in high energy heavy ion collisions seem to reach thermal equilibrium so quickly. An assembly of Hagedorn states is formed in elementary hadronic or heavy ion collisions at hadronization. Microscopic simulations within the transport model UrQMD allow to study the time evolution of such a pure non-equilibrated Hagedorn state gas towards a thermally equilibrated Hadron Resonance Gas by using dynamics, which unlike strings, fully respect detailed balance. Propagation, repopulation, rescatterings and decays of Hagedorn states provide the yields of all hadrons up to a mass of m=2.5 GeV. Ratios of feed down corrected hadron multiplicities are compared to corresponding experimental data from the ALICE collaboration at LHC. The quick thermalization within t=1-2 fm\c of the emerging Hadron Resonance Gas exposes Hagedorn states as a tool to understand hadronization.
Hagedorn states are characterized by being very massive hadron-like resonances and by not being limited to quantum numbers of known hadrons. To generate such a zoo of different Hagedorn states, a covariantly formulated bootstrap equation is solved by ensuring energy conservation and conservation of baryon number $B$, strangeness $S$ and electric charge $Q$. The numerical solution of this equation provides Hagedorn spectra, which enable to obtain the decay width for Hagedorn states needed in cascading decay simulations. A single (heavy) Hagedorn state cascades by various two-body decay channels…
In recent years Hagedorn states have been used to explain the physics close to the critical temperature within a hadron gas. Because of their large decay widths these massive resonances lower $η/s$ to near the AdS/CFT limit within the hadron gas phase. A comparison of the Hagedorn model to recent lattice results is made and it is found that for both Tc =176 MeV and Tc=196 MeV, the hadrons can reach chemical equilibrium almost immediately, well before the chemical freeze-out temperatures found in thermal fits for a hadron gas without Hagedorn states. In this paper we also observe the effects of…
Hagedorn states (HS) are a tool to model the hadronization process which occurs in the phase transition phase between the quark gluon plasma (QGP) and the hadron resonance gas (HRG). Their abundance is believed to appear near the Hagedorn temperature $T_H$ which in our understanding equals the critical temperature $T_c$. These hadron-like resonances are characterized by being very massive and by not being limited to quantum numbers of known hadrons. To generate a whole zoo of such new states we solve the covariantly formulated bootstrap equation by regarding energy conservation and conservatio…
In this work, we have studied the isothermal compressibility ($κ_T$) as a function of temperature, baryon chemical potential and centre-of-mass energy ($\sqrt{s_{NN}}$) using hadron resonance gas (HRG) and excluded-volume hadron resonance gas (EV-HRG) models. A mass cut-off dependence of isothermal compressibility has been studied for a physical resonance gas. Further, we study the effect of heavier resonances ($>$ 2 GeV) on the isothermal compressibility by considering the Hagedorn mass spectrum, $ρ(m)\sim{\exp(bm)}/{(m^2+m_0^2)^{5/4}}$. Here, the parameters, $b$ and $m_0$ are extracted after…
The Hagedorn temperature, T_H is determined from the number of hadronic resonances including all mesons and baryons. This leads to a stable result T_H = 174 MeV consistent with the critical and the chemical freeze-out temperatures at zero chemical potential. We use this result to calculate the speed of sound and other thermodynamic quantities in the resonance hadron gas model for a wide range of baryon chemical potentials following the chemical freeze-out curve. We compare some of our results to those obtained previously in other papers.
Hagedorn states (HS) are a tool to model the hadronization process which occurs in the phase transition region between the quark gluon plasma (QGP) and the hadron resonance gas (HRG). These states are believed to appear near the Hagedorn temperature $T_H$ which in our understanding equals the critical temperature $T_c$. A covariantly formulated bootstrap equation is solved to generate the zoo of these particles characterized baryon number $B$, strangeness $S$ and electric charge $Q$. These hadron-like resonances are characterized by being very massive and by not being limited to quantum number…
A microcanonical treatment of Hagedorn systems, i.e. finite mass hadronic resonances with an exponential mass spectrum controlled by the Hagedorn temperature $T_H$, is performed. We show that, in the absence of any restrictions, a Hagedorn system is a perfect thermostat, i.e. it imparts its temperature $T_H$ to any other system in thermal contact with it. We study the thermodynamic effects of the lower mass cut-off in the Hagedorn mass spectrum. We show that in the presence of a single Hagedorn resonance the temperature of any number of $N_B$ Boltzmann particles differs only slightly from $T_H…
We analyze the light-flavor particle mass spectra and show that in the region up to ~1.8GeV the Hagedorn temperature for baryons is about 30% smaller than for mesons, reflecting the fact that the number of baryon states grows more rapidly with the mass. We also show that the spectra are well reproduced in a model where hadrons are compound objects of quanta, whose available number increases with mass. The rapid growth of number of hadronic states is a combinatorial effect. We also point out that an upper limit on the excitation energy of these quanta results in a maximum number of hadron state…
The physical processes behind the production of light nuclei in heavy ion collisions are unclear. The nice theoretical description of experimental yields by thermal models conflicts with the very small binding energies of the observed states, being fragile in such a hot and dense environment. Other available ideas are delayed production via coalescence, or a cooling of the system after the chemical freeze-out according a Saha equation, or a `quench' instead of a thermal freeze-out. A recently derived prescription of an (interacting) Hagedorn gas is applied to consolidate the above pictures. Th…
A novel, unorthodox picture of the dynamics of heavy ion collisions is developed using the concept of Hagedorn states. A prescription of the bootstrap of Hagedorn states respecting the conserved quantum numbers baryon number B, strangeness S, isospin I is implememted into the GiBUU transport model. Using a strangeness saturation suppression factor suitable for nucleon-nucleon-collisions, recent experimental data for the strangeness production by the HADES collaboration in Au+Au and Ar+KCl is reasonable well described. The experimental observed exponential slopes of the energy distributions are…
Due to long chemical equilibration times within standard hadronic reactions during the hadron gas phase in relativistic heavy ion collisions it has been suggested that the hadrons are "born" into equilibrium after the quark gluon plasma phase. Here we develop a dynamical scheme in which possible Hagedorn states contribute to fast chemical equilibration times of baryon anti-baryon pairs (as well as kaon anti-kaon pairs) inside a hadron gas and just below the critical temperature. Within this scheme, we use master equations and derive various analytical estimates for the chemical equilibration t…
We present a study of transverse momentum ($p_{T}$) spectra of unidentified charged particles in pp collisions at RHIC and LHC energies from $\sqrt{s}$ = 62.4 GeV to 13 TeV using Tsallis/Hagedorn function. The power law of Tsallis/Hagedorn form gives excellent description of the hadron spectra in $p_{T}$ range from 0.2 to 300 GeV/$c$. The power index $n$ of the $p_T$ distributions is found to follow a function of the type $a+b/\sqrt {s}$ with asymptotic value $a = 5.72$. The parameter $T$ governing the soft bulk contribution to the spectra remains almost same over wide range of collision energ…
It is shown that large Nc QCD must have a Hagedorn spectrum (i.e. a spectrum of hadron which grows exponentially with the hadrons mass) provided that certain technical assumptions concerning the applicability of perturbation theory to a certain class of correlation functions apply. The basic argument exploits the interplay of confinement and asymptotic freedom.
We bring up the fact that the bulk thermal properties of the hadron gas, as measured on the lattice, preclude a very fast rising of the number of resonance states in the QCD spectrum, as assumed by the Hagedorn hypothesis, unless a substantial repulsion between hadronic resonances is present. If the Hagedorn growth continued above masses ~1.8 GeV, then the thermodynamic functions would noticeably depart from the measured lattice values at temperatures above 140 MeV, just below the transition temperature to quark-gluon plasma.
Hadron resonance gas models provide a good description of the equation of state of quantum chromodynamics determined by lattice QCD calculations at temperatures $T \sim 100-155$ MeV. In this paper we investigate the effects of an exponentially increasing hadron mass spectrum (Hagedorn spectrum) on the azimuthal anisotropy of the rapidly expanding matter formed in ultrarelativistic heavy ion collisions. If the temperature at which the conversion from fluid degrees of freedom to hadrons is sufficiently close to the Hagedorn temperature, the production of Hagedorn resonances suppresses the differ…
The fireball concept of Rolf Hagedorn, developed in the 1960's, is an alternative description of hadronic matter. Using a recently derived mass spectrum, we use the transport model GiBUU to calculate the shear viscosity of a gas of such Hagedorn states, applying the Green-Kubo method to Monte-Carlo calculations. Since the entropy density is rising ad infinitum near $T_H$, this leads to a very low shear viscosity to entropy density ratio near $T_H$. Further, by comparing our results with analytic expressions, we find a nice extrapolation behavior, indicating that a gas of Hagedorn states comes …
We argue that two seemingly different phenomena, namely the well-known saturation of the Hagedorn exponential distribution and the less familiar saturation of Regge trajectories at resonance masses $m\approx$ 2-2.5 GeV are related and have the same origin: quark deconfinement. We show that the slope of the real part of non-linear Regge trajectories determines the prefactor $f(m)$ in Hagedorn's resonance mass density distribution $ρ(m)$. While the Hagedorn distribution comes from statistics, Regge trajectories contain dynamics.
The Monte Carlo results in lattice QCD for the pressure and energy density at small temperature $T < 155$ MeV and zero baryonic chemical potential are analyzed within the hadron resonance gas model. Two extensions of the ideal hadron resonance gas are considered: the excluded volume model which describes a repulsion of hadrons at short distances and Hagedorn model with the exponential mass spectrum. Considering both of these models one by one we do not find the conclusive evidences in favor of any of them. The controversial results appear because of rather different sensitivities of the pressu…
To describe the transverse distribution of charged hadrons at 1.96 TeV observed by the CDF collaboration, we propose a formula with two component, namely, hadron gas distributions and inverse power laws. The data collected at 0.9, 2.76, 7, and 13 TeV by the ALICE, CMS, and ATLAS collaborations are also analyzed using various models including single component models as well as two component models. The results by using modified version of Hagedorn's formula are compared with those by using the two component model proposed by Bylinkin, Rostovtsev and Ryskin (BRR). Moreover, we show that there is…
Using a Hagedorn resonance gas picture and quark-hadron duality we estimate the dilepton emission rate in the vicinity of the QCD deconfinement phase transition. The result is then used to calculate a dilepton spectrum in ultrarelativistic heavy ion collisions. We show that multibody contributions taken into account in the Hagedorn resonance gas approach provide an enhancement of the production rate of massive dileptons as compared to the previously considered sources.
A scenario of heavy resonances, called massive Hagedorn states, is proposed which exhibits a fast ($t\approx 1$ fm/c) chemical equilibration of (strange) baryons and anti-baryons at the QCD critical temperature $T_c$. For relativistic heavy ion collisions this scenario predicts that hadronization is followed by a brief expansion phase during which the equilibration rate is higher than the expansion rate, so that baryons and antibaryons reach chemical equilibrium before chemical freeze-out occurs.
We review the resonance gas formalism of hadron thermodynamics and recall that an exponential increase of the resonance spectrum leads to a limiting temperature of hadronic matter. We then show that the number p(n) of ordered partitions of an integer n grows exponentially with n and satisfies the integer counterpart of the statistical bootstrap equation. Considering the set of all partitions as a Gibbs ensemble provides a partition thermodynamics which is also governed by a limiting temperature, determined by the combinatorial structure of the problem. Further associating intrinsic quantum num…
We show how excited states in QCD can be profitably used to build up the Polyakov loop in the fundamental representation at temperatures below the hadron-quark-gluon crossover. The conditions under which a Hagedorn temperature for the Polyakov loop can be defined are analysed.
An effective model reproducing the equation of state of hadronic matter as obtained in recent lattice QCD simulations and from hadron resonance gas data is presented. The hadronic phase is described by means of an extended Mott-Hagedorn resonance gas while the QGP phase is described by the extended PNJL model. The dissociation of hadrons is obtained by including the state dependent hadron resonance width. The model gives a quantitative estimate for partial fractions of hadronic and partonic degrees of freedom above $T_c$.
A combined effective model reproducing the equation of state of hadronic matter as obtained in recent lattice QCD simulations is presented. The model reproduces basic physical characteristics encountered in dense hadronic matter in the quark-gluon plasma (QGP) phase and the lower temperature hadron resonance gas phase. The hadronic phase is described by means of an extended Mott-Hagedorn resonance gas while the QGP phase is described by the extended PNJL model. The dissociation of hadrons is obtained by including the state dependent hadron resonance width.
The present status of soft hadron production in high energy heavy-ion collisions is summarized. In spite of strong evidence for extensive dynamical evolution and collective expansion of the fireball before freeze-out I argue that its chemical composition is hardly changed by hadronic final state interactions. The measured hadron yields thus reflect the primordial conditions at hadronization. The observed production pattern is consistent with statistical hadronization at the Hagedorn temperature from a state of uncorrelated, color deconfined quarks and antiquarks, but requires non-trivial chemi…
We study the equation of state (EoS) of the hot and dense hadron gas by incorporating the excluded volume corrections into the ideal hadron resonance gas model (HRG). The total hadron mass spectrum of the model is the sum of discrete mass spectrum consisting all the experimentally known hadrons and the exponentially rising continuous Hagedorn states. We confront the EoS of the model with lattice quantum chromodynamics (LQCD) results at finite baryon chemical potential. We find that this modified HRG model reproduce the LQCD results up to T = 160 MeV at zero as well as finite baryon chemical po…
In the context of the Hagedorn temperature half-centenary I describe our understanding of the hot phases of hadronic matter both below and above the Hagedorn temperature. The first part of the review addresses many frequently posed questions about properties of hadronic matter in different phases, phase transition and the exploration of quark-gluon plasma (QGP). The historical context of the discovery of QGP is shown and the role of strangeness and strange antibaryon signature of QGP illustrated. In the second part I discuss the corresponding theoretical ideas and show how experimental results…
A hadron resonance gas model including all known particles and resonances with masses $m<2$ GeV and an exponentially rising density of Hagedorn states for $m>2$ GeV is used to obtain an upper bound on the shear viscosity to entropy density ratio, $η/s\approx1/(4π)$, of hadronic matter near $T_c$. We found a large trace anomaly and small speed of sound near $T_c$, which agree well with recent lattice calculations. We comment on the bulk viscosity to entropy density ratio close to $T_c$.
The structure of the hadron resonances attracts much attention, in association with the recent observations of various exotic hadrons which do not fit well in the conventional picture. These findings urge us to consider various new configurations such as the multiquark states and the hadronic molecules. However, it is a subtle problem to define a proper classification scheme for the hadron structure, and the nonzero decay width of the hadron resonances makes the analysis complicated. In this paper, we summarize the recent developments in the studies of the structure of the hadron resonances, f…
We discuss the interacting hadron resonance gas model to describe the thermodynamics of hadronic matter. While the attractive interaction between hadrons is taken care of by including all the resonances with zero width, the repulsive interactions are included by considering density-dependent mean field potentials. The bulk thermodynamic quantities are confronted with the lattice quantum chromodynamics simulation results at zero as well as at finite baryon chemical potential. We further estimate the shear and bulk viscosity coefficients of hot and dense hadronic matter within the ambit of this …
An overview of a hadron resonance gas (HRG) model that includes van der Waals interactions between hadrons is presented. Applications of the excluded volume HRG model to heavy-ion collision data and lattice QCD equation of state are discussed. A recently developed quantum van der Waals hadron resonance gas model is covered as well. Applications of this model in the context of the QCD critical point are elaborated.
We discuss the composite nature of hadrons appearing near the s-wave two-hadron threshold. Generalizing the Weinberg's weak-binding relation for stable bound states, we show that the compositeness of near-threshold resonances and quasi-bound states can be determined by observable quantities.
We present the systematic analysis of transverse momentum ($p_T$) spectra of identified hadrons in p+p collisions at RHIC ($\sqrt{s}$ = 62.4 and 200 GeV) and at LHC energies ($\sqrt{s}$ = 0.9, 2.76 and 7.0 TeV) using phenomenological fit functions. We review various forms of Hagedorn and Tsallis distributions and show their equivalence. We use Tsallis distribution which successfully describes the spectra in p+p collisions using two parameters, Tsallis temperature $T$ which governs the soft bulk spectra and power $n$ which determines the initial production in partonic collisions. We obtain thes…
We present a study of the effects of magnetic fields on fluctuations and correlations in hadron resonance gas model. We find significant changes in the fluctuations of net baryon number, electric charge and strangeness. This is also reflected in various fluctuation ratios along the freezeout curve.
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 reproduce the lattice QCD data quite satisfactorily.
Results related to the possible chemical equilibration of hadrons in heavy ion collisions are reviewed. Overall the evidence is very strong with a few clear and well-documented deviations, especially concerning multi-strange hadrons. Two effects are considered in some detail. Firstly, the neglect of (possibly an infinite number) of heavy resonances is investigated with the help of the Hagedorn model. Secondly, possible deviations from the standard statistical distributions are investigated by considering in detail results obtained using the Tsallis distribution.
We present, in the framework of the interacting hadron resonance gas, an evaluation of thermodynamical quantities. The interaction is modelled via a correction for the finite size of the hadrons. We investigate the sensitivity of the model calculations on the radius of the hadrons, which is a parameter of the model. Our calculations for thermodynamical quantities as energy and entropy densities and pressure are confronted with predictions using the lattice Quantum Chromodynamics (QCD) formalism.
We examine the stability of hadron resonance gas models by extending them to take care of undiscovered resonances through the Hagedorn formula. We find that the influence of unknown resonances on thermodynamics is large but bounded. Hadron resonance gases are internally consistent up to a temperature higher than the cross over temperature in QCD; but by examining quark number susceptibilities we find that their region of applicability seems to end even below the QCD cross over. We model the decays of resonances and investigate the ratios of particle yields in heavy-ion collisions. We find that…
A detailed discussion of recent results obtained within the hadron resonance gas model with the multi-component hard core repulsion is presented. Among them there are the adiabatic chemical freeze-out criterion, the concept of separate chemical freeze-out of strange particles and the effects of enhancement and sharpening of wide resonances and quark gluon bags occurring in a thermal medium. These findings are discussed in order to strengthen the planned heavy-ion collision experimental programs at low collision energies. We argue, that due to found effects, at the center of mass collision ener…
The description of the production of light (anti-)(hyper-)nuclei in a hadron resonance gas, or statistical-thermal model approach, has proven to be rather successful, despite the fact that the binding energies of these compound objects are small compared to the emitting fireball temperature. We summarise some recent developments and findings in this approach.
Chiral quark models with Polyakov loop at finite temperature have been often used to describe the phase transition. We show how the transition to a hadron resonance gas is realized based on the quantum and local nature of the Polyakov loop.
We study to what extent a measurement of the $m_\bot$ spectra for hadrons and their resonances can resolve ambiguities in statistical model description of particle production. We describe in quantitative analysis how physical assumptions about the freeze-out geometry and dynamics influence the particle spectra. Considering ratios of $m_\bot$ distribution of resonance-particle ratios (such as $K^*/K$, $Σ^*/Λ, η'/η$) we observe significant sensitivity to fireball freeze-out geometry and flow dynamics.
Recent developments in hadron spectroscopy triggers the discussion on various exotic configurations beyond the simple three-quark state for baryons and quark-anti-quark pair for mesons. In particular, the states observed near a two-hadron threshold are often regarded as candidates of hadronic molecules, which are made of constituent hadrons and dynamically generated by the hadronic interactions. However, identification of the hadronic molecules involves several subtle difficulties which are often overlooked or underestimated. Here we summarize these subtleties and present a promising approach …
We have explored some phenomenological issues during calculations of transport coefficients for hadronic matter, produced in the experiments of heavy ion collisions. Here, we have used an ideal hadron resonance gas model to demonstrate the issues. On the basis of dissipation mechanism, the hadronic zoo is classified into resonance and non-resonance members, who participate in dissipation via strong decay and scattering channels respectively. Imposing our phenomenological restriction, we are able to provide a rough upper and lower bound estimations of transport coefficients. Interestingly, we f…
We present an effective model for the generic behaviour of hadron masses and phase shifts at finite temperature which shares basic features with recent developments within the PNJL model for correlations in quark matter. On this basis we obtain the transition between a hadron resonance gas phase and the quark gluon plasma in the spirit of the generalized Beth-Uhlenbeck approach where the Mott dissociation of hadrons is encoded in the hadronic phase shifts. Here we restrict ourselves to low-lying hadronic channels and perform a discussion of recent lattice QCD thermodynamics results from this p…
We investigate the effects of finite baryon chemical potential on the transport properties of a hadron resonance gas. We find that a hadron resonance gas with large baryon number density is closer to the ideal fluid limit than the corresponding gas with zero baryon number. This suggests that the system created at the Relativistic Heavy Ion Collider (RHIC) at lower collision energies may behave as a fluid, with an effective fluidity close to the one found at RHIC's highest energy near phase transition. This might explain why the differential elliptic flow coefficient measured at lower collision…
The van der Waals interaction is implemented in a Hadron Resonance Gas model. It is shown that this model can describe Lattice QCD data of different thermodynamical quantities satisfactorily with the van der Waals parameters $a = 1250 \pm 150$ MeV fm$^3$ and $r = 0.7 \pm 0.05$ fm. Further, a phase transition is observed in this model with the critical point at temperature, $T = 62.1$ MeV and baryon chemical potential, $μ_B = 708$ MeV.
Charged particles $p_T$ spectra and elliptic flow in 0-60% Au+Au collisions at RHIC are analyzed in a hydrodynamic model with hot, hadronic resonance gas in the initial state. Physically conceivable hadronic resonance gas, thermalized in the time scale $τ_i$=1 fm, at a (central) temperature $T_i$=220 MeV, with viscosity to entropy ratio $η/s$=0.24, reasonably well explains $p_T$ spectra in all the collision centralities. Centrality dependence of elliptic flow however demands continual increase of viscosity to entropy ratio with centrality.
We analyze the sensitivity of thermal fits to heavy-ion hadron yield data of ALICE and NA49 collaborations to the systematic uncertainties in the hadron resonance gas (HRG) model related to the modeling of the eigenvolume interactions. We find a surprisingly large sensitivity in extraction of chemical freeze-out parameters to the assumptions regarding eigenvolumes of different hadrons. We additionally study the effect of including yields of light nuclei into the thermal fits to LHC data and find even larger sensitivity to the modeling of their eigenvolumes. The inclusion of light nuclei yields…
We show that if the hadronic resonance gas (HRG), with viscosity to entropy ratio $η/s\approx$0.24, is physical at temperature $T\approx$220 MeV, charged particles $p_T$ spectra and elliptic flow in Au+Au collisions at RHIC, over a wide range of collision centrality do not distinguish between initial QGP fluid and initial hadronic resonance gas. Unambiguous identification of bulk of the matter produced in Au+Au collisions require clear demonstration that HRG is unphysical at temperature $T<$200 MeV. It calls for precise lattice simulations with realistic boundary conditions.
A unified equation of state for quark-hadron matter is presented in the generalized Beth-Uhlenbeck form. It follows from a $Φ-$derivable approach to the thermodynamic potential where the ansatz for the $Φ$ functional contains all 2PI diagrams at two-loop order formed with quark cluster Green's functions for quark, diquark, meson and baryon propagators. We present numerical results using an effective model for the generic behaviour of hadron masses and phase shifts at finite temperature which shares basic features with recent developments within the PNJL model for correlations in quark matter. …
We compare recent lattice results on fluctuations and correlations of strangeness, baryon number and electric charge obtained with p4 improved staggered action with the prediction of hadron resonance gas model. We show that hadron resonance gas can describe these fluctuations reasonably well if the hadron properties are as calculated on the lattice.
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.
We show that a measurement of the reaction energy dependence of relative hadron resonance yields in heavy ion collisions can be used to study the phase structure of the dense QCD matter created in these collisions, and investigate the origin of the trends observed in the excitation functions of certain soft hadronic observables. We show that presence of chemical nonequilibrium in light quark abundance imparts a characteristic signature on the energy dependence of resonance yields, that differs considerably from what is expected in the equilibrium picture.
