This study investigates transverse-momentum (pT) distributions of pi-, pi+, K-, K+, p, pbar, K0s, and Lambda in several centrality classes of Pb-Pb collisions at sqrt(sNN) = 2.76 TeV. The measured spectra are analyzed with the Tsallis non-extensive distribution, from which the effective temperature T, non-extensive parameter q, and the mean transverse momentum mean_pT are extracted for each particle species and centrality interval. To disentangle thermal and collective effects, the mean kinetic freeze-out temperature T0 is obtained from the intercept of the T-versus-mass relation, while the average transverse flow velocity betaT is extracted from the slope of mean_pT versus the mean moving mass for pions, kaons, and protons.
The results show that T increases and q decreases with increasing centrality, indicating a hotter and more equilibrated system in central collisions. A clear mass dependence of T supports a multi-freeze-out scenario, with heavier particles decoupling earlier. Both T0 and betaT rise from peripheral to mid-central collisions before saturating toward central events, which may suggest the onset of collective behavior or changes in freeze-out dynamics. These observations provide new insights into the thermal and dynamical properties of the medium created in heavy-ion collisions at the LHC.
We consider Tsallis cosmology as an approach to thermodynamic gravity and derive the bound on the Tsallis parameter to be $β<2$ by using the constraints derived from the formation of the primordial light elements, Helium, Deuterium and Litium, from the observational data from Big Bang Nucleosynthesis (BBN) which allows only a very tiny deviation from General Relativity (GR). Next we consider thermal dark matter (DM) freeze-out mechanism in Tsallis cosmological era and derive bounds on the Tsallis parameter from the observed DM relic abundance to be $1-β< 10^{-5}$.
The thermodynamic parameters like energy density, pressure, entropy density, temperature and particle density are determined from the transverse momentum distributions of charged particles in Pb-Pb collisions at the LHC. The results show a clear increase with the centrality and the beam energy in all parameters. It is determined that in the final freeze-out stage the energy density reaches a value of about 0.039 GeV/fm$^3$ for the most central collisions at $\sqrt{s_{NN}}$ = 5.02 TeV. This is less than that at chemical freeze-out where the energy density is about 0.36 GeV/fm$^3$. This decrease…
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 redundancy 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…
The transverse momentum distributions measured in $p-p$ collisions at the LHC determine the kinetic freeze-out stage of the collision. The parameters deduced from these distributions differ from those determined at chemical freeze-out. The present investigation focuses on the chemical potentials at kinetic freeze-out, these are not necessarily zero as they are at chemical freeze-out, the only constraint is that they should be equal for particles and antiparticles at LHC energies. The thermodynamic variables are determined in the framework of the Tsallis distribution. The chemical potentials in…
High energy heavy-ion collisions in laboratory produce a form of matter that can test Quantum Chromodynamics (QCD), the theory of strong interactions, at high temperatures. One of the exciting possibilities is the existence of thermodynamically distinct states of QCD, particularly a phase of de-confined quarks and gluons. An important step in establishing this new state of QCD is to demonstrate that the system has attained thermal equilibrium. We present a test of thermal equilibrium by checking that the mean hadron yields produced in the small impact parameter collisions as well as grand cano…
The kinetic freeze-out temperatures, $T_0$, in nucleus-nucleus collisions at the Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) energies are extracted by four methods: i) the Blast-Wave model with Boltzmann-Gibbs statistics (the BGBW model), ii) the Blast-Wave model with Tsallis statistics (the TBW model), iii) the Tsallis distribution with flow effect (the improved Tsallis distribution), and iv) the intercept in $T=T_0+am_0$ (the alternative method), where $m_0$ denotes the rest mass and $T$ denotes the effective temperature which can be obtained by different distribut…
In this article, we will present a systematic analysis of transverse momentum spectra of the strange hadron in different multiplicity events produced in pp collision at $\sqrt{s}$ = 7 TeV, pPb collision at $\sqrt{s_{NN}}$ = 5.02 TeV and PbPb collision at $\sqrt{s_{NN}}$ = 2.76 TeV. The differential freeze out scenario of strange hadron $K^{0}_{s}$ assumed while analyzing the data using a Tsallis distribution which is modified to include transverse flow. The $p_{T}$ distributions of strange hadron in different systems are characterized in terms of the parameters namely, Tsallis temperature ($T$…
If the interaction rates between the visible and the dark sectors were never strong enough, the observed dark matter relic abundance could have been produced in the early Universe by non-thermal processes. This is what occurs in the so-called freeze-in mechanism. In the simplest version of the freeze-in paradigm, after dark matter is produced from the standard model thermal bath, its abundance is frozen and remains constant. However, thermalization and number-changing processes in the dark sector can have strong impacts, in particular enhancing the dark matter relic abundance by several orders…
We analyse the transverse momentum ($p_{\rm T}$)-spectra as a function of charged-particle multiplicity at midrapidity ($|y| < 0.5$) for various identified particles such as $π^{\pm}$, $K^{\pm}$, $K_S^0$, $p+\overline{p}$, $ϕ$, $K^{*0} + \overline {K^{*0}}$, and $Λ$ + $\barΛ$ in proton-proton collisions at $\sqrt{s}$ = 7 TeV using Boltzmann-Gibbs Blast Wave (BGBW) model and thermodynamically consistent Tsallis distribution function. We obtain the multiplicity dependent kinetic freeze-out temperature ($T_{\rm kin}$) and radial flow ($β$) of various particles after fitting the $p_{\rm T}$-distri…
The transverse momentum spectra of charged pions, kaons, and protons produced at mid-rapidity in central nucleus-nucleus (AA) collisions at high energies are analyzed by considering particles to be created from two participant partons which are assumed to be contributors from the collision system. Each participant (contributor) parton is assumed to contribute to the transverse momentum by a Tsallis-like function. The contributions of the two participant partons are regarded as the two components of transverse momentum of the identified particle. The experimental data measured in high-energy AA…
In the present work, we study the recent collision energy and multiplicity dependence of the charged particle transverse momentum spectra as measured by the ALICE collaboration in $pp$ collisions at $\sqrt{s}$ = 5.02 and 13 TeV using the non-extensive Tsallis distribution and the Boltzmann-Gibbs Blast Wave (BGBW) model. A thermodynamically consistent form of the Tsallis distribution is used to extract the kinetic freeze-out parameters from the transverse momentum spectra of charged particles at mid-rapidity. In addition, a comprehensive study of fitting range dependence of transverse momentum …
We analyzed the transverse momentum {\ppt} spectra of different particle species containing strange quark {\ks}, {\lam (\alam)} and {\xim ({\axi})} in different centrality intervals at mid-rapidity ($y$) from {\auau} collisions at {\sqrtsNN}= 54.4 GeV. The {\ppt} spectra of these strange hadrons are investigated by Tsallis-like distribution. The Tsallis-like distribution satisfactorily fits the experimental data. The effective temperature, entropy based parameter $q$ and mean {\ppt} extracted from the Tsallis-like distribution function while the kinetic freeze-out temperature ($T_0$) and trans…
The nature of dark matter (DM) and how it might interact with the particles of the Standard Model (SM) is one of greatest mysteries currently facing particle physics, and addressing these issues should provide some understanding of how the observed relic abundance was produced. One widely considered production mechanism, a weakly interacting massive particle (WIMP) produced as a thermal relic, provides a target cross section for DM annihilation into SM particles by solving the Boltzmann equation. In this thermal freeze-out mechanism, dark matter is produced in thermal equilibrium with the SM i…
WIMP-like Dark Matter Without Thermalization At Freeze-Out
University of Wisconsin, Madison（威斯康星大学麦迪逊分校）；Wisconsin IceCube Particle Astrophysics Center (WIPAC), University of Wisconsin, Madison（威斯康星冰立方粒子天体物理中心，威斯康星大学麦迪逊分校）；Fermi National Accelerator Laboratory（费米国家加速器实验室）；Kavli Institute for Cosmological Physics, University of Chicago（芝加哥大学卡弗里宇宙物理学研究所）；Department of Astronomy and Astrophysics, University of Chicago（芝加哥大学天文与天体物理系）；Texas Center for Cosmology and Astroparticle Physics, Weinberg Institute for Theoretical Physics, Department of Physics, The University of Texas at Austin（德克萨斯大学奥斯汀分校物理系温伯格理论物理研究所宇宙线与高能天体物理中心）
Transverse momentum spectra of negative and positive pions produced at mid-(pseudo)rapidity in inelastic or non-single-diffractive proton-proton collisions over a center-of-mass energy, $\sqrt{s}$, range from a few GeV to above 10 TeV are analyzed by the blast-wave fit with Boltzmann (Tsallis) distribution. The blast-wave fit results are well fitting to the experimental data measured by several collaborations. In a particular superposition with Hagedorn function, both the excitation functions of kinetic freeze-out temperature ($T_0$) of emission source and transverse flow velocity ($β_T$) of p…
Multiplicity Dependence of Non-extensive Parameters for Strange and Multi-Strange Particles in Proton-Proton Collisions at $\sqrt{s}= 7$ TeV at the LHC
We investigate the transverse momentum ($p_{\rm T}$) spectra of identified hadrons in minimum-bias proton-proton (pp) collisions at a centre-of-mass energy ($\sqrt{s}$) of 0.9, 2.76, 5.02, 7 and 13 TeV in the framework of Tsallis-blast wave (TBW) model. It is found that the model describes well the particle spectra up to 10 GeV/c. The radial flow ($\langle β\rangle$) increases with the collision energy. The degrees of non-equilibrium ($q$) and the Tsallis temperature parameter ($T$) show a similar behaviour, but with a much weaker trend. With this dependence of the freeze-out parameters on the…
Kinetic freeze-out temperature and flow velocity extracted from transverse momentum spectra of final-state light flavor particles produced in collisions at RHIC and LHC
Transverse momentum spectra of proton, deuteron and triton in gold-gold (Au-Au) collisions at 54.4 GeV are analyzed in different centrality bins by the blast wave model with Tsallis statistics. The model results are approximately in agreement with the experimental data measured by STAR Collaboration in special transverse momentum ranges. We extracted the kinetic freeze out temperature, transverse flow velocity and freeze out volume from the transverse momentum spectra of the particles. It is observed that the kinetic freeze out temperature is increasing from central to peripheral collisions. H…
We used blast wave model with Tsallis statistics to analyze the experimental data measured by ALICE Collaboration in proton-proton collisions at Large Hadron Collider and extracted the related parameters (kinetic freeze-out temperature, transverse flow velocity and kinetic freeze-out volume of emission source) from transverse momentum spectra of the particles. We found that the kinetic freeze-out temperature and kinetic freeze-out volume are mass dependent. The former increase while the latter decrease with the particle mass which is the evidence of a mass as well as volume differential kineti…
Hadronic freezeout during the evolution of the medium created in heavy-ion collisions is an important phenomena. It is quite useful to find a universal freezeout condition for each and every nuclear collisions. In this article, we have constructed a hybrid model to calculate the ratio of transverse energy to total mean multiplicity $E_{T} /N_{ch}$, since this ratio can possibly act as a freezeout condition in heavy-ion collision experiments. Present hybrid model blends two approaches : Tsallis statistics and wounded quark approach. Recently, Tsallis statistics has been reliably used to obtain …
The transverse momentum (mass) spectra of the multi-strange and non-multi-strange (i.e. other identified) particles in central gold-gold (Au-Au), lead-lead (Pb-Pb), argon-muriate (Ar-KCl) and nickel-nickel (Ni-Ni) collisions over a wide energy range have been studied in this work. The experimental data measured by various collaborations have been analyzed. The blast-wave fit with Tsallis statistics is used to extract the kinetic freeze-out temperature and transverse flow velocity from the experimental data of transverse momentum (mass) spectra. The extracted parameters increase with the increa…
Collectivity Signatures in High-Multiplicity pp Collisions from Hybrid Hydro+Tsallis Modeling of Pion Spectra
Abdul Wali Khan University Mardan（马尔丹阿卜杜勒瓦利汗大学）；Princess Nourah bint Abdulrahman University（公主努拉·宾特·阿卜杜勒拉赫曼大学）；Hubei University of Automotive Technology（湖北汽车工业学院）
We collected the transverse momentum (mass) spectra of charged hadrons ($π^{-}$, $π^{+}$, $K^{-}$, $K^{+}$, $\overline{p}$, and $p$) produced in collisions over a center-of-mass energy range from 2.70 to 200 GeV (per nucleon pair). The modified Tsallis--Pareto-type function (the TP-like function) with average transverse flow velocity is used to describe the contribution of participant or constituent quarks to transverse momentum of considered hadron. The experimental spectra of $π^{\mp}$ and $K^{\mp}$ (or $\overline{p}$ and $p$) are fitted by the convolution of two (or three) TP-like functions…
We analyzed the transverse momentum spectra of proton, deuteron and triton in Boron-Boron (B-B), Oxygen-Oxygen (O-O), and Calcium-Calcium (Ca-Ca) central collisions, as well as in several centrality bins in Gold-Gold (Au-Au) collisions at 39 GeV by using the blast wave model with Tsallis statistics. The bulk properties in terms of kinetic freeze-out temperature, transverse flow velocity and kinetic freeze-out volume are extracted from the model by the least square method. We observed that with increasing the rest mass of the particle, the kinetic freeze-out temperature becomes larger, while tr…
Transverse momentum spectra of negative and positive pions produced at mid-(pseudo)rapidity in inelastic or non-single-diffractive proton-proton collisions and in central nucleus-nucleus collisions over an energy range from a few GeV to above 10 TeV are analyzed by a (two-component) blast-wave model with Boltzmann-Gibbs statistics and with Tsallis statistics respectively. The model results are in similarly well agreement with the experimental data measured by a few productive collaborations who work at the Heavy Ion Synchrotron (SIS), Super Proton Synchrotron (SPS), Relativistic Heavy Ion Coll…
We investigate the identified hadrons transverse momentum ($p_{\rm T}$) spectra in Pb-Pb (Pb-Pb, Xe-Xe, p-Pb) collisions at $\sqrt{s_{\rm NN}}=$ 2.76 (5.02, 5.44, 5.02) TeV in the framework of Tsallis-blast wave (TBW) model with a linear transverse velocity profile and with a constant velocity profile. In this model, the Tsallis temperature ($T$), the average radial flow velocity ($\langle β\rangle$) and the degree of non-equilibrium ($q$) of the system are common for all hadrons when a combined fit is performed to the $p_{\rm T}$ spectra of different particles at a given centrality. It is fou…
Transverse momentum spectra of different types of identified charged particles in central Gold-Gold (Au-Au) collisions, and inelastic (INEL) or non-single-diffrative (NSD) proton-proton (pp) collisions at the Relativistic Heavy Ion Collider (RHIC), as well as in central and peripheral Lead-Lead (Pb-Pb) collisions, and INEL or NSD pp collisions at the Large Hadron Collider (LHC) are analyzed by the blast wave model with Tsallis statistics. The model results are approximately in agreement with the experimental data measured by STAR, PHENIX and ALICE Collaborations in special transverse momentum …
Transverse momentum spectra of $π^+$, $K^+$, $p$, $K^0_s$, $Λ$, $Ξ$ or $\barΞ^+$ and $Ω$ or $\barΩ^+$ or $Ω+\barΩ$ in Copper-Copper (Cu-Cu), Gold-Gold (Au-Au) and Lead-Lead (Pb-Pb) collisions at 200 GeV, 62.4 GeV and 2.76 TeV respectively, are analyzed in different centrality bins by the blast wave model with Tsallis statistics. The model results are approximately in agreement with the experimental data measured by BRAHMS, STAR and ALICE Collaborations in special transverse momentum ranges. Kinetic freeze out temperature, transverse flow velocity and kinetic freezeout volume are extracted from…
Thermodynamic Analysis of Transverse Momentum Spectra in Pb-Pb Collisions at 2.76 TeV: Centrality Dependence of Temperature, Freezeout Parameters and Non-Extensitivity
Kinetic Freeze-Out Properties from Transverse Momentum Spectra of kaon, Pion, and (anti-)proton production in U+U collisions at $\sqrt{s_{NN}}$ = 193 GeV
Recent observations of QGP-like conditions in high-multiplicity pp collisions from ALICE experiment at the LHC warrants an introspection whether to use pp collisions as a baseline measurement to characterize heavy-ion collisions for possible formation of a Quark-Gluon Plasma. A double differential study of the particle spectra and thermodynamics of the produced system as a function of charged-particle multiplicity and transverse spherocity in pp collisions would shed light into the underlying event dynamics. Transverse spherocity, one of the event shape observables, allows to separate the even…
