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Register a new userThermalization of Hadrons via Hagedorn States
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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.
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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.
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.
Bound state perturbation theory is well established for QED atoms. Today the hyperfine splitting of Positronium is known to $O(alpha^7logalpha)$. Whereas standard expansions of scattering amplitudes start from free states, bound states are expanded around eigenstates of the Hamiltonian including a binding potential. The eigenstate wave functions have all powers of $alpha$, requiring a choice in the ordering of the perturbative expansion. Temporal $(A^0=0)$ gauge permits an expansion starting from valence Fock states, bound by their instantaneous gauge field. This formulation is applicable in any frame and seems promising even for hadrons in QCD. The $O(alpha_s^0)$ confining potential is determined (up to a universal scale) by a homogeneous solution of Gauss law.
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.
The exciting discovery by LHCb of the $P_c(4312)^+$ and $P_c(4450)^+$ pentaquarks, or the suggestion of a tetraquark nature for the $Z_c(3900)$ state seen at BESIII and Belle, have triggered a lot of activity in the field of hadron physics, with new experiments planned for searching other exotic mesons and baryons, and many theoretical developments trying to disentangle the true multiquark nature from their possible molecular origin. After a brief review of the present status of these searches, this paper focusses on recently seen or yet to be discovered exotic heavy baryons that may emerge from a conveniently unitarized meson-baryon interaction model in coupled channels. In particular, we will show how interferences between the different coupled-channel amplitudes of the model may reveal the existence of a $N^*$ resonance around 2 GeV having a meson-baryon quasi-bound state nature. We also discuss the possible interpretation of some of the $Omega_c$ states recently discovered at LHCb as being hadron molecules. The model also predicts the existence of doubly-charmed quasibound meson-baryon $Xi_{cc}$ states, which would be excited states of the ground-state $Xi_{cc}(3621)$ MeV, whose mass has only been recently established. Extensions of these results to the bottom sector will also be presented.
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