scholarly journals THE HAGEDORN TEMPERATURE REVISITED

2011 ◽  
Vol 26 (16) ◽  
pp. 1197-1209 ◽  
Author(s):  
J. CLEYMANS ◽  
D. WORKU
Keyword(s):  
Speed Of Sound ◽  
Chemical Potential ◽  
Thermodynamic Quantities ◽  
Chemical Potentials ◽  
Wide Range ◽  
Hadron Gas ◽  
Hadronic Resonances ◽  
Stable Result ◽  
Chemical Freeze ◽  
Freeze Out

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.

scholarly journals Probing chemical freeze-out criteria in relativistic nuclear collisions with coarse grained transport simulations

2020 ◽  
Vol 56 (10) ◽  
Author(s):  
Tom Reichert ◽  
Gabriele Inghirami ◽  
Marcus Bleicher
Keyword(s):  
Chemical Potential ◽  
Transport Model ◽  
Relativistic Quantum ◽  
Coarse Graining ◽  
Coarse Grained ◽  
Quantum Molecular Dynamics ◽  
Novel Approach ◽  
Relativistic Nuclear Collisions ◽  
Chemical Freeze ◽  
Freeze Out

AbstractWe introduce a novel approach based on elastic and inelastic scattering rates to extract the hyper-surface of the chemical freeze-out from a hadronic transport model in the energy range from E$$_\mathrm {lab}=1.23$$ lab = 1.23  AGeV to $$\sqrt{s_\mathrm {NN}}=62.4$$ s NN = 62.4  GeV. For this study, the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model combined with a coarse-graining method is employed. The chemical freeze-out distribution is reconstructed from the pions through several decay and re-formation chains involving resonances and taking into account inelastic, pseudo-elastic and string excitation reactions. The extracted average temperature and baryon chemical potential are then compared to statistical model analysis. Finally we investigate various freeze-out criteria suggested in the literature. We confirm within this microscopic dynamical simulation, that the chemical freeze-out at all energies coincides with $$\langle E\rangle /\langle N\rangle \approx 1$$ ⟨ E ⟩ / ⟨ N ⟩ ≈ 1  GeV, while other criteria, like $$s/T^3=7$$ s / T 3 = 7 and $$n_\mathrm {B}+n_{\bar{\mathrm {B}}}\approx 0.12$$ n B + n B ¯ ≈ 0.12 fm$$^{-3}$$ - 3 are limited to higher collision energies.

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

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Deeptak Biswas
Keyword(s):  
Hadron Collider ◽  
Heavy Ion ◽  
Strange Particle ◽  
Relativistic Heavy Ion Collider ◽  
Yield Data ◽  
Central Collisions ◽  
Chemical Potentials ◽  
Beam Energy Scan ◽  
Chemical Freeze ◽  
Freeze Out

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.

scholarly journals Influence of hadronic resonances on the chemical freeze-out in heavy-ion collisions

2020 ◽  
Vol 101 (5) ◽  
Author(s):  
P. Alba ◽  
V. Mantovani Sarti ◽  
J. Noronha-Hostler ◽  
P. Parotto ◽  
I. Portillo-Vazquez ◽  
...  
Keyword(s):  
Heavy Ion Collisions ◽  
Heavy Ion ◽  
Ion Collisions ◽  
Hadronic Resonances ◽  
Chemical Freeze ◽  
Freeze Out

scholarly journals Novel Unexpected Reconstructions of (100) and (111) Surfaces of NaCl: Theoretical Prediction

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Alexander G. Kvashnin ◽  
Dmitry G. Kvashnin ◽  
Artem R. Oganov
Keyword(s):  
Crystal Morphology ◽  
Chemical Potential ◽  
Rehbinder Effect ◽  
High Chemical ◽  
Chemical Potentials ◽  
Wide Range ◽  
Surface Phases ◽  
Charge Analysis ◽  
Bader Charge Analysis ◽  
Very High

Abstract We have predicted stable reconstructions of the (100) and (111) surfaces of NaCl using the global optimization algorithm USPEX. Several new reconstructions, together with the previously reported ones, are found. For the cleaved bare (100) surface, pure Na and pure Cl are the only stable surface phases. Our study of the (111) surface shows that a newly predicted Na3Cl-(1 × 1) reconstruction is thermodynamically stable in a wide range of chlorine chemical potentials. It has a sawtooth-like profile where each facet reproduces the (100) surface of rock-salt NaCl, hinting on the preferred growth of the (100) surface. We used Bader charge analysis to explain the preferable formation of this sawtooth-like Na3Cl-(1 × 1) reconstruction of the (111) surface of NaCl. We find that at a very high chemical potential of Na, the polar (and normally absent) (111) surface becomes part of the equilibrium crystal morphology. At both very high and very low chemical potentials of Cl, we predict a large decrease of surface energy and fracture toughness (the Rehbinder effect).

scholarly journals Tsallis Statistics in High Energy Physics: Chemical and Thermal Freeze-Outs

Physics ◽  
2020 ◽  
Vol 2 (4) ◽  
pp. 654-664
Author(s):  
Jean Cleymans ◽  
Masimba Wellington Paradza
Keyword(s):  
High Energy Physics ◽  
Chemical Potential ◽  
High Energy ◽  
Pp Collisions ◽  
Proton Proton ◽  
Wide Range ◽  
Relativistic Proton ◽  
System Temperature ◽  
Tsallis Distribution ◽  
Freeze Out

We present an overview of a proposal in relativistic proton-proton (pp) collisions emphasizing the thermal or kinetic freeze-out stage in the framework of the Tsallis distribution. In this paper we take into account the chemical potential present in the Tsallis distribution by following a two step procedure. In the first step we used the redudancy present in the variables such as the system temperature, T, volume, V, Tsallis exponent, q, chemical potential, μ, and performed all fits by effectively setting to zero the chemical potential. In the second step the value q is kept fixed at the value determined in the first step. This way the complete set of variables T,q,V and μ can be determined. The final results show a weak energy dependence in pp collisions at the centre-of-mass energy s=20 TeV to 13 TeV. The chemical potential μ at kinetic freeze-out shows an increase with beam energy. This simplifies the description of the thermal freeze-out stage in pp collisions as the values of T and of the freeze-out radius R remain constant to a good approximation over a wide range of beam energies.

scholarly journals Hadronic equation of state and speed of sound in thermal and dense medium

2014 ◽  
Vol 29 (27) ◽  
pp. 1450152 ◽  
Author(s):  
Abdel Nasser Tawfik ◽  
Hend Magdy
Keyword(s):  
Equation Of State ◽  
Specific Heat ◽  
High Temperatures ◽  
Speed Of Sound ◽  
Chemical Potential ◽  
Dense Medium ◽  
Thermodynamic Quantities ◽  
Strange Hadron ◽  
The Difference ◽  
Grand Canonical

The equation of state p(ϵ) and speed of sound squared [Formula: see text] are studied in grand canonical ensemble of all hadron resonances having masses ≤2 GeV . This large ensemble is divided into strange and non-strange hadron resonances and furthermore to pionic, bosonic and fermionic sectors. It is found that the pions represent the main contributors to [Formula: see text] and other thermodynamic quantities including the equation of state p(ϵ) at low temperatures. At high temperatures, the main contributions are added in by the massive hadron resonances. The speed of sound squared can be calculated from the derivative of pressure with respect to the energy density, ∂p/∂ϵ, or from the entropy-specific heat ratio, s/cv. It is concluded that the physics of these two expressions is not necessarily identical. They are distinguishable below and above the critical temperature Tc. This behavior is observed at vanishing and finite chemical potential. At high temperatures, both expressions get very close to each other and both of them approach the asymptotic value, 1/3. In the hadron resonance gas (HRG) results, which are only valid below Tc, the difference decreases with increasing the temperature and almost vanishes near Tc. It is concluded that the HRG model can very well reproduce the results of the lattice quantum chromodynamics (QCD) of ∂p/∂ϵ and s/cv, especially at finite chemical potential. In light of this, energy fluctuations and other collective phenomena associated with the specific heat might be present in the HRG model. At fixed temperatures, it is found that [Formula: see text] is not sensitive to the chemical potential.

scholarly journals Energy Dependence of Particle Ratios in High Energy Nucleus-Nucleus Collisions: A USTFM Approach

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Inam-ul Bashir ◽  
Rameez Ahmad Parra ◽  
Hamid Nanda ◽  
Saeed Uddin
Keyword(s):  
Particle Production ◽  
Chemical Potential ◽  
Heavy Ion ◽  
High Energy ◽  
Ion Collisions ◽  
System A ◽  
Particle Ratios ◽  
High Degree ◽  
Chemical Freeze ◽  
Freeze Out

We study the identified particle ratios produced at mid-rapidity (y<0.5) in heavy-ion collisions, along with their correlations with the collision energy. We employ our earlier proposed unified statistical thermal freeze-out model (USTFM), which incorporates the effects of both longitudinal and transverse hydrodynamic flow in the hot hadronic system. A fair agreement seen between the experimental data and our model results confirms that the particle production in these collisions is of statistical nature. The variation of the chemical freeze-out temperature and the baryon chemical potential with respect to collision energies is studied. The chemical freeze-out temperature is found to be almost constant beyond the RHIC energy and is found to be close to the QCD predicted phase-transition temperature suggesting that the chemical freeze-out occurs soon after the hadronization takes place. The vanishing value of chemical potential at LHC indicates very high degree of nuclear transparency in the collision.

scholarly journals Possible interrelations among chemical freeze-out conditions

2016 ◽  
Vol 25 (03) ◽  
pp. 1650018 ◽  
Author(s):  
A. Tawfik ◽  
M. Y. El-Bakry ◽  
D. M. Habashy ◽  
M. T. Mohamed ◽  
E. Abbas
Keyword(s):  
Physical Meaning ◽  
Thermal Equilibrium ◽  
Chemical Potential ◽  
High Energy ◽  
Baryon Chemical Potential ◽  
Particle Ratios ◽  
Hadron Mass ◽  
Low Energies ◽  
Chemical Freeze ◽  
Freeze Out

At thermal equilibrium, different chemical freeze-out conditions have been proposed so far. They have an ultimate aim of proposing a universal description for the chemical freeze-out parameters ([Formula: see text] and [Formula: see text]), which are to be extracted from the statistical fitting of different particle ratios measured at various collision energies with calculations from thermal models. A systematic comparison between these conditions is presented. The physical meaning of each of them and their sensitivity to the hadron mass cuts are discussed. Based on availability, some of them are compared with recent lattice calculations. We found that most of these conditions are thermodynamically equivalent, especially at small baryon chemical potential. We propose that further crucial consistency tests should be performed at low energies. The fireball thermodynamics is another way of guessing conditions describing the chemical freeze-out parameters extracted from high-energy experiments. We endorse the possibility that the various chemical freeze-out conditions should be interpreted as different aspects of one universal condition.

scholarly journals On the Higher Moments of Particle Multiplicity, Chemical Freeze-Out, and QCD Critical Endpoint

2013 ◽  
Vol 2013 ◽  
pp. 1-22 ◽  
Author(s):  
A. Tawfik
Keyword(s):  
Lower Order ◽  
Thermal Evolution ◽  
Order Moment ◽  
Particle Multiplicity ◽  
Higher Moments ◽  
Third Order ◽  
Chemical Potentials ◽  
Dynamical Fluctuation ◽  
Chemical Freeze ◽  
Freeze Out

We calculate the first six nonnormalized moments of particle multiplicity within the framework of the hadron resonance gas model. In terms of the lower order moments and corresponding correlation functions, general expressions of higher order moments are derived. Thermal evolution of the first four normalized moments and their products (ratios) are studied at different chemical potentials, so that it is possible to evaluate them at chemical freeze-out curve. It is found that a nonmonotonic behaviour reflecting the dynamical fluctuation and strong correlation of particles starts to appear from the normalized third order moment. We introduce novel conditions for describing the chemical freeze-out curve. Although the hadron resonance gas model does not contain any information on the criticality related to the chiral dynamics and singularity in the physical observables, we are able to find out the location of the QCD critical endpoint atμ~350 MeV and temperatureT~162 MeV.

Roberge–Weiss phase transition and QCD phase diagram in the (2 + 1) flavor Polyakov quark meson model

2019 ◽  
Vol 34 (02) ◽  
pp. 1950011
Author(s):  
Xiu-Fei Li
Keyword(s):  
Phase Transition ◽  
Phase Diagram ◽  
Chemical Potential ◽  
Polyakov Loop ◽  
Effective Model ◽  
Thermodynamic Quantities ◽  
Qcd Phase Diagram ◽  
Chemical Potentials

The Roberge–Weiss (RW) phase transition of (2 + 1) flavor QCD at imaginary quark chemical potentials [Formula: see text] is investigated by employing the Polyakov loop extended Quark Meson model (PQM), where [Formula: see text] is temperature, and [Formula: see text] is a dimensionless chemical potential. We calculate some thermodynamic quantities and draw the phase diagram. This work can be considered as a supplement of studying the RW transition by using the effective model.

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