Freeze-out Temperature Research Articles

Rapidity and Energy Dependencies of Temperatures and Volume Extracted from Identified Charged Hadron Spectra in Proton-Proton Collisions at a Super Proton Synchrotron (SPS).

The standard (Bose-Einstein/Fermi-Dirac, or Maxwell-Boltzmann) distribution from the relativistic ideal gas model is used to study the transverse momentum (pT) spectra of identified charged hadrons (π-, π+, K-, K+, 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 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 (Teff or T), kinetic freeze-out temperature (T0), and initial temperature (Ti) decrease with the increase in rapidity and increase with the increase in c.m. energy. The kinetic freeze-out volume (V) extracted from the π-, π+, K-, K+, and 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.

Multiplicity Dependence of the Freeze-Out Parameters in Symmetric and Asymmetric Nuclear Collisions at Large Hadron Collider Energies

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 Teff and T0 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,T0,βT) 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.

Evolution of effective temperature, kinetic freeze-out temperature and transverse flow velocity in pp collision

This article focuses on the study of strange hadrons ( ) at 0.2 TeV, recorded by STAR at RHIC, and at 0.9 TeV, 5.02 TeV and 7 TeV, recorded by CMS at LHC, in pp collision in the rapidity range from 0 to 2. The pT distributions of these strange particles have been processed using two statistical models, the Tsallis and the modified Hagedorn model. Both models fit the experimental data well. We extracted different freezeout parameters from the fit procedure using the abovementioned functions. We found that with increasing the collision energy, the effective temperature (T), in the case of the Tsallis model, and kinetic/thermal freeze-out temperature (T0) and transverse flow velocity (β T), in the case of the modified Hagedorn model, increase because of greater energy transfer among the participants at higher colliding energies. Both T and T0 are observed to increase with the increase in the rest masses of the outgoing particles revealing the multi-freeze-out scenario. Furthermore, the multiplicity parameter (N0) decreases with the increase in the particle mass, confirming the mass differential freeze-out scenario. An inverse relationship between the non-extensivity parameter (q) and the masses of the produced particles has been noticed. Similarly, an inverse correlation between q and T has been found. For lighter particles, smaller T and greater q mean that they decouple from the system later and attain equilibrium slowly compared to heavier ones. In addition, a positive correlation between β T and T0 is noticed, which agrees with the literature.

Perturbative aspects of mass dimension one fermions non-minimally coupled to electromagnetic field

This paper addresses perturbative aspects of the renormalization of a fermion with mass dimension one non-minimally coupled to the electromagnetic field. Specifically, we calculate the one-loop corrections to the propagators and vertex functions of the model and determine the one-loop beta function of the non-minimal electromagnetic coupling. Additionally, we perform calculations of the two-loop corrections to the gauge field propagator, demonstrating that it remains massless and transverse up to this order. We also find that the non-minimal electromagnetic coupling can exhibit asymptotic freedom if a certain condition is satisfied. As a potential dark matter candidate, these findings suggest that the field may decouple at high energies. This aspect holds significance for calculating the relic abundance and freeze-out temperature of the field, particularly in relation to processes involving the ordinary particles of the Standard Model.

Excitation Function of Freeze-Out Parameters in Symmetric Nucleus–Nucleus and Proton–Proton Collisions at the Same Collision Energy

We analyze the transverse momentum (pT) spectra of π+, π−, K+, K−, p, p¯, Λ, Λ¯, Ξ, Ξ¯, Ω−, Ω¯+ or Ω−+Ω¯+ 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 (q), the mean transverse momentum spectra (⟨pT⟩), the multiplicity parameter (N0), kinetic freeze-out temperature (T0) and transverse flow velocity (βT). We reported a plateau structure of pT, T, T0, βT, pT 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.

Completing RHINO

The right-handed (RH) Higgs-induced neutrino mixing (RHINO) model explains neutrino masses and origin of matter in the universe within a unified picture. The mixing, effectively described by a dimension five operator, is responsible both for the production of dark neutrinos, converting a small fraction of seesaw neutrinos acting as source, and for their decays. We show that including the production of source neutrinos from Higgs portal interactions, their abundance can thermalise prior to the onset of source-dark neutrino oscillations, resulting into an enhanced production of dark neutrinos that thus can play the role of decaying dark matter (DM) for a much higher seesaw scale. This can be above the sphaleron freeze-out temperature and as high as ~ 100 TeV, so that strong thermal resonant leptogenesis for the generation of the matter-antimatter asymmetry is viable. We obtain a ~ 1 TeV–1 PeV allowed dark neutrino mass range. Intriguingly, their decays can also explain a neutrino flux excess at mathcal{O} (100 TeV) energies recently confirmed by the IceCube collaboration analysing 7.5 yr HESE data. Our results also point to an effective scale for Higgs portal interactions nicely identifiable with the grandunified scale and many orders of magnitude below the effective scale for the mixing. We explain this hierarchy in a UV-complete model with a very heavy fermion as mediator: the first scale corresponds to the fundamental scale of new physics, while the second is much higher because of a very small coupling that can be identified with a symmetry breaking parameter. Therefore, RHINO realises a simple unified model of neutrino masses and origin of matter in the universe currently under scrutiny at neutrino telescopes and potentially embeddable within a grandunified model.

Simulation Studies of Track-Based Analysis of Charged Particles in Symmetric Hadron–Hadron Collisions at 7 TeV

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 (Teff)) from the Tsallis–Pareto-kind function and T02 (kinetic freezeout temperature) from the Hagedorn function. The temperatures are affected by pT as well Nch cuts.

Dilution of dark matter relic density in singlet extension models

We study the dilution of dark matter (DM) relic density caused by the electroweak first-order phase transition (FOPT) in the singlet extension models, including the singlet extension of the standard model (xSM), of the two-Higgs-doublet model (2HDM+S) and the next-to-minimal supersymmetric standard model (NMSSM). We find that in these models the entropy released by the strong electroweak FOPT can dilute the DM density to 1/3 at most. Nevertheless, in the xSM and NMSSM where the singlet field configure is relevant to the phase transition temperature, the strong FOPT always happens before the DM freeze-out, making the dilution effect negligible for the current DM density. We derive an analytical upper bound on the freeze-out temperature and a numerical lower bound on nucleation temperature in the xSM. On the other hand, in the 2HDM+S where the DM freeze-out temperature is independent of FOPT, the dilution may salvage some parameter space excluded by excessive DM relic density or by DM direct detections.

New models and big bang nucleosynthesis constraints in f(Q) gravity

The f(Q) theories of modified gravity arise from the consideration of non-metricity as the basic geometric quantity, and have been proven to be very efficient in describing the late-time Universe. We use the Big Bang Nucleosynthesis (BBN) formalism and observations in order to extract constraints on various classes of f(Q) models. In particular, we calculate the deviations that f(Q) terms bring on the freeze-out temperature T_f in comparison to that of the standard Lambda CDM evolution, and then we impose the observational bound on left| frac{delta {T}_f}{{T}_f}right| to extract constraints on the involved parameters of the considered models. Concerning the polynomial model, we show that the exponent parameter should be negative, while for the power-exponential model and the new hyperbolic tangent-power model we find that they pass the BBN constraints trivially. Finally, we examine two DGP-like f(Q) models, and we extract the bounds on their model parameters. Since many gravitational modifications, although able to describe the late-time evolution of the Universe, produce too-much modification at early times and thus fall to pass the BBN confrontation, the fact that f(Q) gravity can safely pass the BBN constraints is an important advantage of this modified gravity class.

Dependence of Freeze-Out Parameters on Collision Energies and Cross-Sections

We analyzed the transverse momentum spectra (pT) 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 (βT), the kinetic freeze-out temperature (T0), and the kinetic freeze-out volume (V) from the pT spectra using the BGBW model. Furthermore, we also obtained the initial temperature (Ti) and the mean transverse momentum (<pT>) by the alternative method. We observed that T0 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.

Ratio of baryon and electric-charge cumulants at second order with acceptance corrections

We evaluate the ratio of baryon and electric-charge cumulants at second order from the recent experimental results at sNN=200 GeV by the STAR Collaboration. The baryon number cumulant is reconstructed from the proton number distribution, and effects of the finite acceptance on the transverse momentum are corrected assuming the independent particle emission. We show that the obtained ratio has a dependence on the rapidity window. Comparison of the result with the hadron resonance gas model and lattice QCD numerical simulations suggests that if the fluctuations are generated from a thermal medium its temperature is significantly lower than the chemical freezeout temperature.

Observation of non-homogeneous scenarios for different temperatures in hadron(nucleus)-nucleus collisions at RHIC and LHC energies

We used the modified Hagedron function and analyzed the experimental data measured by the BRAHMS, STAR, PHENIX, and ALICE Collaborations in Copper-Copper, Gold-Gold, deuteron-Gold, Lead-Lead, proton-Lead and proton–proton collisions, and extracted the related parameters (kinetic freezeout temperature, transverse flow velocity, kinetic freezeout volume, mean transverse momentum, and initial temperature) from the transverse momentum spectra of the particles (non-strange and strange particles). We observed that all the above parameters increase from peripheral to central collisions, except transverse flow velocity, which remains unchanged. The kinetic freezeout temperature depends on the particle’s interaction cross-section such that a larger cross-section corresponds to a smaller T 0 and reveals the two kinetic freezeout scenarios. Similarly, the initial temperature follows the mass dependency of the particle, and it increases with the particle mass. The transverse flow velocity and mean transverse momentum depend on the particle’s mass. The former decreases while the latter increases with the mass of the particle. Furthermore, different freezeout surfaces for different particles are observed as the kinetic freezeout volume decrease for heavier particles. We also extracted the entropy index-parameter “ n ” and the parameter N 0 , the former remains almost unchanged while the latter decreases from central collisions to the periphery. Furthermore, the kinetic freezeout temperature, transverse flow velocity, kinetic freezeout volume, initial temperature, mean transverse momentum and the parameter N 0 at LHC are larger than that of RHIC, showing their dependence on the collision cross-section and collision energy. • The modified Hagedron function analyzes the experimental data measured by the BRAHMS, STAR, PHENIX, and ALICE Collaborations in different collision systems and energies. • Kinetic freeze-out temperature (T 0 ), transverse flow velocity ( β T ), kinetic freeze-out volume (V), mean transverse momentum (<p T >), and initial temperature (Ti) are extracted from the transverse momentum spectra of the particles. • The parameters increase from peripheral to central collisions, except transverse flow velocity, which remains unchanged. • The T 0 is cross-section dependent. A larger cross-section corresponds to a smaller T 0 and reveals the two kinetic freeze scenarios while the initial temperature increases with the particle’s mass. • The β T and <p T > depend on the particle mass. The former decrease while the latter increase. • Furthermore, different freeze-out surfaces for different particles are observed as the V decrease for heavier particles. • Furthermore, the parameters at LHC are more significant than at RHIC, showing their dependence on the collision cross-section and energy.

Study of Bulk Properties of Strange Particles in Au+Au Collisions at sNN = 54.4 GeV.

We analyzed the transverse momentum pT spectra of various strange hadrons KS0, Λ(Λ¯) and Ξ-(Ξ¯+) at mid-rapidity (y) in different centrality intervals from Au+Au collisions at sNN= 54.4 GeV. The pT 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 βT, and mean pT along with other parameters that are strongly dependent on centrality and particle specie are extracted. The effective temperature of multi-strange particle (Ξ-(Ξ¯+)) is larger as compared to singly-strange particles Λ(Λ¯) and KS0. Furthermore, the kinetic freeze-out temperature T, transverse flow velocity βT. and mean pT (⟨pT⟩) show a decreasing trend towards lower centrality, while the entropy parameter q increases from central to peripheral collisions. In addition, a positive correlation of ⟨pT⟩ and T and a negative correlation of q and T are also reported.

Gravity and Cosmology in Kaniadakis Statistics: Current Status and Future Challenges.

Kaniadakis statistics is a widespread paradigm to describe complex systems in the relativistic realm. Recently, gravitational and cosmological scenarios based on Kaniadakis (κ-deformed) entropy have been considered, leading to generalized models that predict a richer phenomenology comparing to their standard Maxwell-Boltzmann counterparts. The purpose of the present effort is to explore recent advances and future challenges of Gravity and Cosmology in Kaniadakis statistics. More specifically, the first part of the work contains a review of κ-entropy implications on Holographic Dark Energy, Entropic Gravity, Black hole thermodynamics and Loop Quantum Gravity, among others. In the second part, we focus on the study of Big Bang Nucleosynthesis in Kaniadakis Cosmology. By demanding consistency between theoretical predictions of our model and observational measurements of freeze-out temperature fluctuations and primordial abundances of 4He and D, we constrain the free κ-parameter, discussing to what extent the Kaniadakis framework can provide a successful description of the observed Universe.

Centrality dependence of proton and light nuclei yields as a consequence of baryon annihilation in the hadronic phase

The centrality dependence of the p/π ratio measured by the ALICE Collaboration in 5.02 TeV Pb-Pb collisions indicates a statistically significant suppression with the increase of the charged particle multiplicity once the centrality-correlated part of the systematic uncertainty is eliminated from the data. We argue that this behavior can be attributed to baryon annihilation in the hadronic phase. By implementing the BB¯↔5π reaction within a generalized partial chemical equilibrium framework, we estimate the annihilation freeze-out temperature at different centralities, which decreases with increasing charged particle multiplicity and yields Tann=132±5 MeV in 0-5% most central collisions. This value is considerably below the hadronization temperature of Thad∼160 MeV but above the thermal (kinetic) freeze-out temperature of Tkin∼100 MeV. Baryon annihilation reactions thus remain relevant in the initial stage of the hadronic phase but freeze out before (pseudo-)elastic hadronic scatterings. One experimentally testable consequence of this picture is a suppression of various light nuclei to proton ratios in central collisions of heavy ions.

Universal scaling of kinetic freeze-out parameters across different collision systems at LHC energies* *Supported by the National Natural Science Foundation of China (11905188, 11875143 and 12061141008), the National Key Research and Development Program of China (2016YFE0100900) and the Innovation Fund of Key Laboratory of Quark and Lepton Physics LPL2020P01 (LZ)

In this study, we perform Tsallis Blast-Wave analysis on the transverse momentum spectra of identified hadrons produced in a wide range of collision systems at the Large Hadron Collider (LHC) including pp, pPb, XeXe, and PbPb collisions. The kinetic freeze-out properties varying with event multiplicity are investigated across these systems. We find that the extracted kinetic freeze-out temperature, radial flow velocity, and non-extensive parameter exhibit a universal scaling behavior for these systems with very different geometric sizes, especially when the independent baryon Tsallis non-extensive parameter is considered. This universality may indicate the existence of a unified partonic evolution stage in different collision systems at the LHC energies.

D*/D ratio in heavy ion collisions

In this work we study the $D^*$ and $D$ multiplicities and how they change during the hadron gas phase of heavy ion collisions. With the help of an effective Lagrangian formalism, we calculate the production and absorption cross sections of the $D^*$ and $D$ mesons in a hadronic medium. We compute the time evolution of the abundances and the ratio $D^* /D$. They are approximately constant in time. Also, assuming a Bjorken type cooling and using an empirical relation between the freeze-out temperature and the central multiplicity density, we estimate $D^* /D$ as a function of $ dN /d \eta (\eta =0)$, which represents the system size. We find that, while the number of $D^*$'s and $D$'s grows significantly with the system size, their ratio remains approximately constant. This prediction can be compared with future experimental data. Our results suggest that the charm meson interactions in the hadron gas do not change their multiplicities and consequently these mesons are close to chemical equilibrium.

Deep Level Transient Fourier Spectroscopy (DLTFS) and Isothermal Transient Spectroscopy (ITS) in vertical GaN-on-GaN Schottky barrier diodes

The paper explores the Deep Level Transient Fourier Spectroscopy (DLTFS) capabilities in characterizing electrically active traps in vertical GaN-on-GaN Schottky barrier diodes (SBDs). The capacitance-DLTFS (C-DLTFS) experiments reveal a prominent electron trap T2 at EC – 0.56 eV with a density (NT2) of 8 × 1014 cm−3 and a weak presence of another trap at EC – 0.18 eV (T1) with NT1 = 3.8 × 1013 cm−3 in the SBDs. The C-DLTFS acquired with two emission transients (TE = 20.48 ms and 2.048 s) has resulted in identical trap signatures for T1 and T2. Due to the high NT, the trap T2 at EC - 0.56 eV is identified from the current-DLTFS (I-DLTFS) and thermally stimulated capacitance (TSCAP) measurements. Especially the TSCAP results indicate the carrier freeze-out temperature (T < 75 K) in the GaN material. Furthermore, the carrier emission kinetics of the trap T2 is evaluated by performing isothermal transient spectroscopy at a stabilized temperature. The capture time constant of T2 is estimated from the isothermal transients attained with shorter trap-filling pulse widths (<100 ns).

An asymmetric SIMP dark matter model

In this paper, we construct the first asymmetric strongly interacting massive particles (SIMP) dark matter (DM) model, where a new vector-like fermion and a new complex scalar both having nonzero chemical potentials can be asymmetric DM particles. After the spontaneous breaking of a U(1)D dark gauge symmetry, these two particles can have accidental ℤ4 charges making them stable. By adding one more complex scalar as a mediator between the SIMP DM, the relic density of DM is determined by 3 → 2 and two-loop induced 2 → 2 annihilations in this model. On the other hand, the SIMP DM can maintain kinetic equilibrium with the thermal bath until the DM freeze-out temperature via the new gauge interaction. Interestingly, this model can have a bouncing effect on DM, whereby the DM number density rises after the chemical freeze-out of DM. With this effect, the prediction of the DM self-interacting cross section in this model can be consistent with astrophysical observations, and the ratio of the DM energy density to the baryonic matter energy density can be explained by primordial asymmetries. We also predict the DM-electron elastic scattering cross section that can be used to test this model in future projected experiments.

Compatibility of big bang nucleosynthesis in some modified gravities

This paper is devoted to investigate the implications of Einstein-Aether and modified Hořava–Lifshitz theories of gravity to the formation of light elements in the early universe named as big bang nucleosynthesis. We choose different models from these theories for a detailed investigation of big bang nucleosynthesis epoch and compare it with the observational bounds. That is, we compare the deviation of freeze-out temperature T_{_f} with the Lambda CDM paradigm and use observational bounds on left| frac{Delta T_{_f}}{T_{_f}}right| to inspect constraints on the involved free parameters of these models. We apply Chi-square test on the Hubble parameter H in each model to analyze the compatibility of model parameters with the observations and find consistent results. We find that chosen models of Einstein-Aether gravity and modified Hořava–Lifshitz gravity can satisfy big bang nucleosynthesis constraints and thus constitute a viable cosmology since they can be source for dark energy sector and late-time accelerated expansion.