Search Results (18)

This study presents the investigation of freezeout parameters, namely the kinetic freezeout temperature (T) and transverse flow velocity (${\beta }_T$), in different centrality intervals with fixed as well as with variable flow profile ($n_0$) in the blast-wave model (using Boltzmann Gibbs statistics). The model is used to fit the experimental data of transverse momentum spectra of ${\pi }^{+}$, $K^{+}$, and p in $Au$–$Au$ and $Pb$–$Pb$ collisions at 200 GeV and 2.76 TeV, respectively. In our observation, when the parameter $n_0$ is considered as a free parameter, the parameter T decreases from head-on to peripheral collisions, while it increases towards the periphery if $n_0$ is fixed. In addition, parameter ${\beta }_T$ decreases from central to peripheral collisions in both cases. These findings provide valuable insights into the dynamics of quark-gluon plasma formation and expansion in high-energy nuclear collisions. Moreover, the kinetic freezeout temperature T and the transverse flow velocity ${\beta }_T$ are mass-dependent; while the former becomes larger for massive particles, the latter becomes larger for light particles, showing the mass differential kinetic freezeout scenario. Full article

Utilizing the Modified Hagedorn function with embedded flow, we analyze the transverse momenta ($p_T$) and transverse mass ($m_T$) spectra of ${\pi }^{+}$ in Au–Au, Cu–Cu, and d–Au collisions at $\sqrt{s_{NN}}$ = 200 GeV across various centrality bins. Our study reveals the centrality and system size dependence of key freezeout parameters, including kinetic freezeout temperature $\left(T_0\right)$, transverse flow velocity $\left({\beta }_T\right)$, entropy-related parameter $\left(n\right)$, and kinetic freezeout volume (V). Specifically, $T_0$ and n increase from central to peripheral collisions, while ${\beta }_T$ and V show the opposite trend. These parameters also exhibit system size dependence; $T_0$ and ${\beta }_T$ are smaller in larger collision systems, whereas V is larger. Importantly, central collisions correspond to a stiffer Equation of State (EOS), characterized by larger ${\beta }_T$ and smaller $T_0$, while peripheral collisions indicate a softer EOS. These insights are crucial for understanding the properties of Quark–Gluon Plasma (QGP) and offer valuable constraints for Quantum Chromodynamics (QCD) models at high temperatures and densities. Full article

The standard (Bose–Einstein/Fermi–Dirac, or Maxwell–Boltzmann) distribution from the relativistic ideal gas model is used to study the transverse momentum ($p_T$) spectra of identified charged hadrons (${\pi }^{-}$, ${\pi }^{+}$, $K^{-}$, $K^{+}$, $\overline{p}$, and p) with different rapidities produced in inelastic proton–proton ($pp$) collisions at a Super Proton Synchrotron (SPS). The experimental data measured using the NA61/SHINE Collaboration at the center-of-mass (c.m.) energies $\sqrt{s}=6.3$, 7.7, 8.8, 12.3, and 17.3 GeV are fitted well with the distribution. It is shown that the effective temperature ($T_{eff}$ or T), kinetic freeze-out temperature ($T_0$), and initial temperature ($T_i$) decrease with the increase in rapidity and increase with the increase in c.m. energy. The kinetic freeze-out volume (V) extracted from the ${\pi }^{-}$, ${\pi }^{+}$, $K^{-}$, $K^{+}$, and $\overline{p}$ spectra decreases with the rapidity and increase with the c.m. energy. The opposite tendency of V, extracted from the p spectra, is observed to be increasing with the rapidity and decreasing with the c.m. energy due to the effect of leading protons. Full article

Strange hadron transverse momentum spectra are analyzed in symmetric $pp$ and $PbPb$ and asymmetric $pPb$ collision systems for their dependence on rapidity and event charged-particle multiplicity. The thermodynamically consistent Tsallis models with and without flow velocity are used to reproduce the experimental data, extracting the freeze-out parameters to gain insights into the underlying physics of the collision processes by looking into the parameters change with different multiplicities, particle types, and collision geometries. We found that with an increase in the event multiplicity, the average transverse flow velocity, effective, and kinetic freezeout temperatures increase, with heavier strange particle species exhibiting a more significant increase. The value of the non-extensivity parameter decreases with an increase in the multiplicity of the particles. For heavier particles, larger $T_{eff}$ and $T_0$ and smaller q have been observed, confirming the quick thermalization and equilibrium for massive particles. Furthermore, the differences in parameter values for particle species are more significant in $pp$ and $pPb$ collisions than in $PbPb$ collisions. In addition, in symmetric $pp$ and $PbPb$ collisions, parameter values ($q,T_0,{\beta }_T$) show more significant shifts for heavier particles compared to the lighter ones. In contrast, in asymmetric $pPb$ collisions, both heavier and lighter particles display uniform linear progression. Full article

We analyze the transverse momentum ($p_T$) spectra of ${\pi }^{+}$, ${\pi }^{-}$, $K^{+}$, $K^{-}$, p, $\overline{p}$, $\Lambda$, $\overline{\Lambda }$, $\Xi$, $\overline{\Xi }$, ${\Omega }^{-}$, ${\overline{\Omega }}^{+}$ or ${\Omega }^{-}+{\overline{\Omega }}^{+}$ in different centrality intervals in gold–gold (Au–Au) and lead–lead (Pb–Pb) symmetric collisions at 200 GeV and 2.76 TeV, respectively, by Tsallis–Pareto-type function. Proton–proton collisions at the same centre of mass energies are also analyzed for these particles to compare the results obtained from these systems. The present work extracts the effective temperature T, non-extensivity parameter $\left(q\right)$, the mean transverse momentum spectra ($⟨p_T⟩$), the multiplicity parameter ($N_0$), kinetic freeze-out temperature ($T_0$) and transverse flow velocity (${\beta }_T$). We reported a plateau structure of $p_T$, T, $T_0$, ${\beta }_T$, $p_T$ and q in central collisions. Beyond the plateau region, the excitation function of all the above parameters decreases towards the periphery, except q, which has a reverse trend. The multiplicity parameter is also extracted, which is found to be decreasing towards the periphery from the central collisions. In addition, we observed that the excitation function of pp collisions is nearly the same to that of the most peripheral symmetric nucleus–nucleus collisions at the same colliding energy. Throughout the analyses, the same multiplicity parameters for particles and their antiparticles have been reported, which show the symmetric production of particles and their antiparticles. Full article

This manuscript presents a simulation study of a track-based analysis of the multiplicity distributions of the primary charged particle compared to experimental measurements in symmetric hadron–hadron collisions acquiring maximum energy for the new particle production. The data are compared to the simulations of EPOS, PYTHIA8, Sibyll, and QGSJET under the same conditions. The event generators in the current study are simple parton-based models that incorporate the Reggie–Gribov theory. The latter is a field theory based on the QCD that uses the mechanism of multiple parton interactions. It has been found that the PYTHIA8 model chases the data well in most of the distributions but depends on the momentum and the requirement of charged particles in a given track, due to its feature-like color reshuffling of quarks and gluons through the color re-connection modes and initial and final state radiations by incorporating the parton showers. The EPOS model could also reproduce some spectral regions and presents a good comparison after the PYTHIA8. All the other models could not produce most of the spectra except for the limited region, which also depends on the analysis’s cuts. Besides the model’s prediction, we used Tsallis–Pareto and Hagedorn functions to fit the aforementioned spectra of the charged particles. The fit is applied to the data and models, and their results are compared. We extract the temperature parameter T₀₁ (effective temperature (T_eff)) from the Tsallis–Pareto-kind function and T₀₂ (kinetic freezeout temperature) from the Hagedorn function. The temperatures are affected by p_T as well N_ch cuts. Full article

We analyzed the transverse momentum spectra ($p_T$) reported by the NA61/SHINE and NA49 experiments in inelastic proton–proton ($pp$) and central Lead–Lead ($Pb-Pb$), Argon–Scandium ($Ar-Sc$), and Beryllium–Beryllium ($Be-Be$) collisions with the Blast-wave model with Boltzmann–Gibbs (BWBG) statistics. The BGBW model was in good agreement with the experimental data. We were able to extract the transverse flow velocity (${\beta }_T$), the kinetic freeze-out temperature ($T_0$), and the kinetic freeze-out volume (V) from the $p_T$ spectra using the BGBW model. Furthermore, we also obtained the initial temperature ($T_i$) and the mean transverse momentum (<$p_T$>) by the alternative method. We observed that $T_0$ increases with increasing collision energy and collision cross-section, representing the colliding system’s size. The transverse flow velocity was observed to remain invariant with increasing collision energy, while it showed a random change with different collision cross-sections. In the same way, the kinetic freeze-out volume and mean transverse momentum increased with an increase in collision energy or collision cross-section. The same behavior was also seen in the freeze-out temperature, which increased with increasing collision cross-sections. At chemical freeze-out, we also determined both the chemical potential and temperature and compared these with the hadron resonance gas model (HRG) and different experimental data. We report that there is an excellent agreement with the HRG model and various experiments, which reveals the ability of the fit function to manifest features of the chemical freeze-out. Full article

We analyzed the transverse momentum $p_{\mathrm{T}}$ spectra of various strange hadrons ${\mathrm{K}}_{\mathrm{S}}^0$, $\mathrm{\Lambda }$($\overline{\mathrm{\Lambda }}$) and ${\mathrm{\Xi }}^{-}$(${\overline{\mathrm{\Xi }}}^{+}$) at mid-rapidity (y) in different centrality intervals from Au+Au collisions at $\sqrt{{\mathrm{s}}_{{}_{\mathrm{NN}}}}$= 54.4 GeV. The $p_{\mathrm{T}}$ spectra of these strange hadrons are investigated by the Tsallis-like distribution, which satisfactorily fits the experimental data. The bulk properties of the medium produced in ultra-relativistic heavy-ion collisions at the kinetic freeze-out are reflected by measuring the hadron spectra. The effective temperature T, transverse flow velocity ${\beta }_T$, and mean $p_{\mathrm{T}}$ along with other parameters that are strongly dependent on centrality and particle specie are extracted. The effective temperature of multi-strange particle (${\mathrm{\Xi }}^{-}$(${\overline{\mathrm{\Xi }}}^{+}$)) is larger as compared to singly-strange particles $\mathrm{\Lambda }$($\overline{\mathrm{\Lambda }}$) and ${\mathrm{K}}_{\mathrm{S}}^0$. Furthermore, the kinetic freeze-out temperature T, transverse flow velocity ${\beta }_T$. and mean $p_{\mathrm{T}}$ ($⟨p_T⟩$) show a decreasing trend towards lower centrality, while the entropy parameter q increases from central to peripheral collisions. In addition, a positive correlation of $⟨p_T⟩$ and T and a negative correlation of q and T are also reported. Full article

Dependencies of midrapidity p_t distributions of the charged pions and kaons, protons and antiprotons on charged-particle multiplicity density (<dN_ch/dη>) in inelastic proton-proton collisions at (s)^1/2 = 7 TeV at the LHC, measured by ALICE Collaboration, are investigated. The simultaneous minimum χ² fits with the Tsallis function with thermodynamical consistence and the Hagedorn function with included transverse flow have well-described the p_t spectra of the particle species in the ten studied groups of charged-particle multiplicity density. The effective temperatures, T, of the Tsallis function with thermodynamical consistence have shown a steady rise with increasing the charged-particle multiplicity in proton-proton collisions at (s)^1/2 = 7 TeV, in agreement with the similar result obtained recently in proton-proton collisions at (s)^1/2 = 13 TeV at the LHC. The respective T versus <dN_ch/dη> dependence in proton-proton collisions at (s)^1/2 = 7 TeV is reproduced quite well by the simple power function with the same value (≈ 1/3) of the exponent parameter as that extracted in proton-proton collisions at (s)^1/2 = 13 TeV. The identical power dependence $T~{\epsilon }^{1/3}$ between the initial energy density and effective temperature of the system has been observed in proton-proton collisions at (s)^1/2 = 7 and 13 TeV. We have observed that the transverse radial flow emerges at <dN_ch/dη> ≈ 6 and then increases, becoming substantial at larger multiplicity events in proton-proton collisions at (s)^1/2 = 7 TeV. We have estimated, analyzing T₀ and $⟨{\beta }_t⟩$ versus <dN_ch/dη> dependencies, that the possible onset of deconfinement phase transition in proton-proton collisions at (s)^1/2 = 7 TeV occurs at <dN_ch/dη> ≈ 6.1 ± 0.3, which is close to the corresponding recent estimate (<dN_ch/dη> ≈ 7.1 ± 0.2) in proton-proton collisions at (s)^1/2 = 13 TeV. The corresponding critical energy densities for probable onset of deconfinement phase transition in proton-proton collisions at (s)^1/2 = 7 and 13 TeV at the LHC have been estimated to be 0.67 ± 0.03 and 0.76 ± 0.02 GeV/fm³, respectively. Full article

The transverse momentum spectra of ${\pi }^{+}$ (${\pi }^{-}$)(${\pi }^{+}+{\pi }^{-}$) at 6.3, 17.3, 31, 900 and 7000 GeV are analyzed by the blast-wave model with Tsallis statistics (TBW) in proton-proton collisions. We took the value of flow profile $n_0$ = 1 and 2 in order to see the difference in the results of the extracted parameters in the two cases. Different rapidity slices at 31 GeV are also analyzed, and the values of the related parameters, such as kinetic freeze-out temperature, transverse flow velocity and kinetic freeze-out volume, are obtained. The above parameters rise with the increase of collision energy, while at 31 GeV, they decrease with increasing rapidity, except for the kinetic freeze-out volume, which increases. We also extracted the parameter q, which is an entropy-based parameter, and its rising trend is noticed with increasing collision energy, while at 31 GeV, no specific dependence of q is observed on rapidity. In addition, the multiplicity parameter $N_0$ and mean transverse momentum are extracted, which increase with increasing collision energy and decrease with increasing rapidity. We notice that the kinetic freeze-out temperature and mean transverse momentum are slightly larger with $n_0$ = 2, while the transverse flow velocity is larger in the case of $n_0$ = 1, but the difference is very small and hence insignificant. Full article

We used the blast wave model with the Boltzmann–Gibbs statistics and analyzed the experimental data measured by the NA61/SHINE Collaboration in inelastic (INEL) proton–proton collisions at different rapidity slices at different center-of-mass energies. The particles used in this study were ${\pi }^{+}$, ${\pi }^{-}$, $K^{+}$, $K^{-}$, and $\overline{p}$. We extracted the kinetic freeze-out temperature, transverse flow velocity, and kinetic freeze-out volume from the transverse momentum spectra of the particles. We observed that the kinetic freeze-out temperature is rapidity and energy dependent, while the transverse flow velocity does not depend on them. Furthermore, we observed that the kinetic freeze-out volume is energy dependent, but it remains constant with changing the rapidity. We also observed that all three parameters are mass dependent. In addition, with the increase of mass, the kinetic freeze-out temperature increases, and the transverse flow velocity, as well as kinetic freeze-out volume decrease. Full article

The transverse momentum spectra of different types of particles, ${\pi }^{\pm }$, $K^{\pm }$, p and $\overline{p}$, produced at mid-(pseudo)rapidity in different centrality lead–lead (Pb–Pb) collisions at 2.76 TeV; proton–lead (p–Pb) collisions at 5.02 TeV; xenon–xenon (Xe–Xe) collisions at 5.44 TeV; and proton–proton (p–p) collisions at 0.9, 2.76, 5.02, 7 and 13 TeV, were analyzed by the blast-wave model with fluctuations. With the experimental data measured by the ALICE and CMS Collaborations at the Large Hadron Collider (LHC), the kinetic freeze-out temperature, transverse flow velocity and proper time were extracted from fitting the transverse momentum spectra. In nucleus–nucleus (A–A) and proton–nucleus (p–A) collisions, the three parameters decrease with the decrease of event centrality from central to peripheral, indicating higher degrees of excitation, quicker expansion velocities and longer evolution times for central collisions. In p–p collisions, the kinetic freeze-out temperature is nearly invariant with the increase of energy, though the transverse flow velocity and proper time increase slightly, in the considered energy range. Full article

Transverse momentum spectra of ${\pi }^{+}$, p, $\Lambda$, $\Xi$ or ${\overline{\Xi }}^{+}$, $\Omega$ or ${\overline{\Omega }}^{+}$ and deuteron (d) in different centrality intervals in nucleus–nucleus collisions at the center of mass energy are analyzed by the blast wave model with Boltzmann Gibbs statistics. We extracted the kinetic freezeout temperature, transverse flow velocity and kinetic freezeout volume from the transverse momentum spectra of the particles. It is observed that the non-strange and strange (multi-strange) particles freezeout separately due to different reaction cross-sections. While the freezeout volume and transverse flow velocity are mass dependent, they decrease with the resting mass of the particles. The present work reveals the scenario of a double kinetic freezeout in nucleus–nucleus collisions. Furthermore, the kinetic freezeout temperature and freezeout volume are larger in central collisions than peripheral collisions. However, the transverse flow velocity remains almost unchanged from central to peripheral collisions. Full article

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 collisions by international collaborations are studied. The excitation functions of kinetic freeze-out temperature and transverse flow velocity are extracted. The two parameters increase quickly from ≈3 to ≈10 GeV (exactly from 2.7 to 7.7 GeV) and then slowly at above 10 GeV with the increase of collision energy. In particular, there is a plateau from near 10 GeV to 200 GeV in the excitation function of kinetic freeze-out temperature. Full article

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, $\mu$, 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 $\mu$ can be determined. The final results show a weak energy dependence in $pp$ collisions at the centre-of-mass energy $\sqrt{s}=20$ TeV to 13 TeV. The chemical potential $\mu$ 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. Full article