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Register a new userEquilibration of hadrons in HICs via Hagedorn States
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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 numbers of known hadrons. All hadronic properties like masses, spectral functions etc.are taken from the hadronic transport model Ultra Relativistic Quantum Molecular Dynamics (UrQMD). Decay chains of single Hagedorn states provide a well description of experimentally observed multiplicity ratios of strange and multi-strange particles. In addition, the final energy spectra of resulting hadrons show a thermal-like distribution with the characteristic Hagedorn temperature $T_H$. Box calculations including these Hagedorn states are performed. Indeed, the time scales leading to equilibration of the system are drastically reduced down to 2...5 fm/c.
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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 subsequently into final stable hadrons. All final hadronic observables like masses, spectral functions and decay branching ratios for hadronic feed down are taken from the hadronic transport model UrQMD. Strikingly, the final energy spectra of resulting hadrons are exponential showing a thermal-like distribution with the characteristic Hagedorn temperature.
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. The tabulation of decay rates of Hagedorn states into light nuclei allows to calculate yields usually unaccessable due to very poor Monte Carlo statistics. Decay yields of stable hadrons and light nuclei are calculated. While the scale-free decays of Hagedorn states alone are not compatible with the experimental data, a thermalized hadron and Hagedorn state gas is able to describe the experimental data. Applying a cooling of the system according a Saha-equation with conservation of nucleons and anti-nucleons in number leads to (nearly) temperature independent yields, thus a production of the light nuclei at temperatures much lower than the chemical freeze-out temperature is possible.
In this note, we construct simple stochastic toy models for holographic gauge theories in which distributions of energy on a collection of sites evolve by a master equation with some specified transition rates. We build in only energy conservation, locality, and the standard thermodynamic requirement that all states with a given energy are equally likely in equilibrium. In these models, we investigate the qualitative behavior of the dynamics of the energy distributions for different choices of the density of states for the individual sites. For typical field theory densities of states (log(rho(E)) ~ E^{alpha<1}), the model gives diffusive behavior in which initially localized distributions of energy spread out relatively quickly. For large N gauge theories with gravitational duals, the density of states for a finite volume of field theory degrees of freedom typically includes a Hagedorn regime (log(rho(E)) ~ E). We find that this gives rise to a trapping of energy in subsets of degrees of freedom for parametrically long time scales before the energy leaks away. We speculate that this Hagedorn trapping may be part of a holographic explanation for long-lived gravitational bound states (black holes) in gravitational theories.
The fireball concept of Rolf Hagedorn, developed in the 1960s, 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 close or even below the boundary $1/4pi$ from AdS-CFT.
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 nicely reproduced. Thus, a dynamical model using Hagedorn resonance states, supplemented by a strangeness saturation suppression factor, is able to explain essential features (multiplicities, exponential slope) of experimental data for strangeness production in nucleus-nucleus collisions close to threshold.
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