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

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.

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Freeze-Out Parameters in Heavy-Ion Collisions at AGS, SPS, RHIC, and LHC Energies

Advances in High Energy Physics ◽

10.1155/2015/349013 ◽

2015 ◽

Vol 2015 ◽

pp. 1-20 ◽

Cited By ~ 53

Author(s):

Sandeep Chatterjee ◽

Sabita Das ◽

Lokesh Kumar ◽

D. Mishra ◽

Bedangadas Mohanty ◽

...

Keyword(s):

Transverse Momentum ◽

Heavy Ion Collisions ◽

Heavy Ion ◽

High Energy ◽

Particle Multiplicity ◽

Charged Particle Multiplicity ◽

Ion Collisions ◽

Momentum Distributions ◽

Chemical Freeze ◽

Freeze Out

We review the chemical and kinetic freeze-out conditions in high energy heavy-ion collisions for AGS, SPS, RHIC, and LHC energies. Chemical freeze-out parameters are obtained using produced particle yields in central collisions while the corresponding kinetic freeze-out parameters are obtained using transverse momentum distributions of produced particles. For chemical freeze-out, different freeze-out scenarios are discussed such as single and double/flavor dependent freeze-out surfaces. Kinetic freeze-out parameters are obtained by doing hydrodynamic inspired blast wave fit to the transverse momentum distributions. The beam energy and centrality dependence of transverse energy per charged particle multiplicity are studied to address the constant energy per particle freeze-out criteria in heavy-ion collisions.

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

Advances in High Energy Physics ◽

10.1155/2021/6611394 ◽

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.

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Freeze-out scenarios in small systems at RHIC and LHC energies

International Journal of Modern Physics E ◽

10.1142/s0218301320500068 ◽

2020 ◽

Vol 29 (02) ◽

pp. 2050006

Author(s):

Susil Kumar Panda ◽

Subhasis Samanta ◽

Ajay Kumar Dash ◽

Ranbir Singh ◽

Rita Paikaray ◽

...

Keyword(s):

System Size ◽

Particle Multiplicity ◽

Charged Particle Multiplicity ◽

Suppression Factor ◽

Increase With Increase ◽

Multiplicity Formula ◽

Charge Multiplicity ◽

System Volume ◽

Chemical Freeze ◽

Freeze Out

We study the hadronic yields produced in two small collision systems [Formula: see text] at [Formula: see text][Formula: see text]TeV and [Formula: see text] at [Formula: see text][Formula: see text]TeV, and extracted the chemical freeze-out (CFO) parameters. The CFO parameters are obtained using a hadron resonance gas (HRG) model and in this study present the system size dependence of the parameters. We observe that with the strangeness suppression factor [Formula: see text] included in the model, a single freeze-out scenario can describe hadronic yields for all the centralities of [Formula: see text] collision at [Formula: see text][Formula: see text]TeV, indicating that the strange hadrons have not reached full equilibrium. On the other hand, for small average charged particle multiplicity ([Formula: see text]) bins of [Formula: see text] collision at [Formula: see text][Formula: see text]TeV strangeness is not fully equilibrated whereas strangeness equilibration seems to be reached in large [Formula: see text]. For both the collision systems, no significant system volume dependence of the temperature has been observed. However, in comparable [Formula: see text] values, temperatures are 10–20[Formula: see text]MeV larger for [Formula: see text] collision compared to [Formula: see text] collision. We observe that the volume of the system at the CFO increases with increase of charge multiplicity for both the collisions. The increase is much steeper in [Formula: see text] collision at [Formula: see text][Formula: see text]TeV than [Formula: see text] collision at [Formula: see text][Formula: see text]TeV. Further, we analyze the transverse momentum ([Formula: see text]) spectra of different hadrons produced in [Formula: see text] collision at [Formula: see text][Formula: see text]TeV in a combined freeze-out scenario. We show the [Formula: see text] dependence of freeze-out parameters. It is observed that with [Formula: see text] included in the model, a single freeze-out scheme can describe the [Formula: see text] spectra. For similar [Formula: see text] values, [Formula: see text] in both the collision systems are close to each other and overall values of [Formula: see text] increase with increase of [Formula: see text]. Unlike CFO scenario using the produced hadron yields only, freeze-out temperature in combined scenario of chemical and kinetic freeze-out, obtained from [Formula: see text] spectra, increases with increase of [Formula: see text]. For smaller [Formula: see text] values, the temperature in [Formula: see text] collision at [Formula: see text][Formula: see text]TeV is similar to that of [Formula: see text] collision at [Formula: see text][Formula: see text]TeV. However, temperatures are larger in [Formula: see text] collision than [Formula: see text] collision at larger [Formula: see text] values.

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Higher moments of net-proton multiplicity distributions in heavy ion collisions at chemical freeze-out

Physics Letters B ◽

10.1016/j.physletb.2013.04.018 ◽

2013 ◽

Vol 722 (1-3) ◽

pp. 144-150 ◽

Cited By ~ 47

Author(s):

Jinghua Fu

Keyword(s):

Heavy Ion Collisions ◽

Heavy Ion ◽

Higher Moments ◽

Ion Collisions ◽

Multiplicity Distributions ◽

Chemical Freeze ◽

Freeze Out

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A Baseline Study of the Event-Shape and Multiplicity Dependence of Chemical Freeze-Out Parameters in Proton-Proton Collisions at \( {\sqrt{s}} \) = 13 TeV Using PYTHIA8

Physics ◽

10.3390/physics2040040 ◽

2020 ◽

Vol 2 (4) ◽

pp. 679-694

Author(s):

Rutuparna Rath ◽

Arvind Khuntia ◽

Sushanta Tripathy ◽

Raghunath Sahoo

Keyword(s):

High Energy ◽

Monte Carlo Event ◽

Event Generator ◽

Particle Multiplicity ◽

Event Shape ◽

Charged Particle Multiplicity ◽

Pp Collisions ◽

Proton Proton ◽

Chemical Freeze ◽

Freeze Out

The event-shape and multiplicity dependence of the chemical freeze-out temperature (Tch), freeze-out radius (R), and strangeness saturation factor (γs) are obtained by studying the particle yields from the PYTHIA8 Monte Carlo event generator in proton-proton (pp) collisions at the centre-of-mass s = 13 TeV. Spherocity is one of the transverse event-shape techniques to distinguish jetty and isotropic events in high-energy collisions and helps in looking into various observables in a more differential manner. In this study, spherocity classes are divided into three categories, namely (i) spherocity integrated, (ii) isotropic, and (iii) jetty. The chemical freeze-out parameters are extracted using a statistical thermal model as a function of the spherocity class and charged particle multiplicity in the canonical, strangeness canonical, and grand canonical ensembles. A clear observation of the multiplicity and spherocity class dependence of Tch, R, and γs is observed. A final state multiplicity, Nch≥ 30 in the forward multiplicity acceptance of the ALICE detector appears to be a thermodynamic limit, where the freeze-out parameters become almost independent of the ensembles. This study plays an important role in understanding the particle production mechanism in high-multiplicity pp collisions at the Large Hadron Collider (LHC) energies in view of a finite hadronic phase lifetime in small systems.

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THE HAGEDORN TEMPERATURE REVISITED

Modern Physics Letters A ◽

10.1142/s0217732311035584 ◽

2011 ◽

Vol 26 (16) ◽

pp. 1197-1209 ◽

Cited By ~ 22

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.

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