Search

We explore the spectra of transverse momenta of hadrons with strange quark content (KS0, ϕ, Λ+Λ̄, Ξ̄+Ξ̄+, and Ω−+Ω̄+) produced in proton–proton collisions at sNN = 7 TeV. We applied Tsallis statistics in a blast wave model (TBW) to the ALICE Collaboration’s experimental data and extracted the freezeout parameters (Tsallis temperature, transverse flow velocity, and the parameter q, which is the non-extensive parameter). The changing trend of these parameters is studied with changing multiplicity. The parameter q decreases while the parameter T and βT increases toward higher multiplicities. βT is noted to drop to zero in the system with the lowest multiplicities. In addition, the interrelationships between the parameters T with βT and T with q are presented where the former correlation is positive and the latter one is negative.

We study the transverse momentum (pT) spectra of neutral pions and identified charged hadrons produced in proton–proton (pp), deuteron–gold (d–Au), and gold–gold (Au–Au) collisions at the center of mass energy sNN=200 GeV. The study is made in the framework of a multisource thermal model used in the partonic level. It is assumed that the contribution to the pT-value of any hadron comes from two or three partons with an isotropic distribution of the azimuthal angle. The contribution of each parton to the pT-value of a given hadron is assumed to obey any one of the standard (Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein) distributions with the kinetic freeze-out temperature and average transverse flow velocity. The pT spectra of the final-state hadrons can be fitted by the superposition of two or three components. The results obtained from our Monte Carlo method are used to fit the experimental results of the PHENIX and STAR Collaborations. The results of the present work serve as a suitable reference baseline for other experiments and simulation studies.

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.

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, 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 produced particles obtained from a given selection in the blast-wave fit with Boltzmann distribution have a hill at s ≈ 10 GeV, a drop at dozens of GeV, and then an increase from dozens of GeV to above 10 TeV. However, both the excitation functions of T 0 and β T obtained in the blast-wave fit with Tsallis distribution do not show such a complex structure, but a very low hill. In another selection for the parameters or in the superposition with the usual step function, T 0 and β T increase generally quickly from a few GeV to about 10 GeV and then slightly at above 10 GeV, there is no such the complex structure, when also studying nucleus-nucleus collisions.

We collected the transverse momentum (mass) spectra of charged hadrons (π−, π+, K−, K+, 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∓ and K∓ (or p¯ and p) are fitted by the convolution of two (or three) TP-like functions due to the fact that two (or three) constituent quarks are regarded as two (or three) energy resources in the formation of considered hadron. From the reasonable fits to the spectra, the thermal freeze-out parameters are extracted, and the pseudoentropy is newly defined and extracted. Some parameters quickly change in the energy range of less than 7.7 GeV, and slowly change in the energy range of greater than 7.7 GeV, indicating the variation of collision mechanism at around 7.7 GeV.

In this minireview article, the transverse momentum spectra of final-state particles produced in high-energy hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions described by the multisource thermal model at the quark or parton level are summarized. In the model, the participant or contributor quarks or partons are considered to contribute together to the transverse momentum distribution of final-state particles with different modes of contributions. The concrete mode of contribution is generally determined by the difference of azimuthal angles of contributor partons in their emissions.

We have studied the transverse momentum (pT) spectra of the final-state strange particles, including K±, ϕ, Ξ, and Ω, produced in high energy lead–lead (Pb–Pb), proton–lead (p–Pb), xenon–xenon (Xe–Xe) collisions at the Large Hadron Collider (LHC). Taking into account the contribution of multiquark composition, whose probability density distribution is described by the modified Tsallis–Pareto-type function; we simulate the pT spectra of the final-state strange particles by a Monte Carlo method, which is shown to be in good agreement with the experimental data in most the cases. The kinetic freeze-out parameters are obtained. The present method provides a new tool for studying the spectra of various particles produced in high energy collisions, reflecting more realistically the collision process, which is of great significance to study the formation and properties of the produced particles.

The squared momentum transfer spectra of light mesons, π0, π+, η, and ρ0, produced in high-energy virtual photon-proton (γ*p) → meson + nucleon process in electron-proton (ep) collisions measured by the CLAS Collaboration are analyzed by the Monte Carlo calculations, where the transfer undergoes from the incident γ* to emitted meson or equivalently from the target proton to emitted nucleon. In the calculations, the Erlang distribution from a multi-source thermal model is used to describe the transverse momentum spectra of emitted particles. Our results show that the average transverse momentum (⟨pT⟩) and the initial-state temperature (Ti) increase from lower squared photon virtuality (Q2) and Bjorken variable (xB) to higher one. This renders that the excitation degree of emission source, which is described by ⟨pT⟩ and Ti, increases with increasing of Q2 and xB.

The differential cross-section in squared momentum transfer of ρ, ρ0, ω, ϕ, f0980, f11285, f01370, f11420, f01500, and J/ψ produced in high-energy virtual photon-proton (γ∗p), photon-proton (γp), and proton-proton (pp) collisions measured by the H1, ZEUS, and WA102 Collaborations is analyzed by the Monte Carlo calculations. In the calculations, the Erlang distribution, Tsallis distribution, and Hagedorn function are separately used to describe the transverse momentum spectra of the emitted particles. Our results show that the initial- and final-state temperatures increase from lower squared photon virtuality to a higher one and decrease with the increase of center-of-mass energy.

With the framework of the multisource thermal model, we analyze the experimental transverse momentum spectra of various jets produced in different collisions at high energies. Two energy sources, a projectile participant quark and a target participant quark, are considered. Each energy source (each participant quark) is assumed to contribute to the transverse momentum distribution to be the TP-like function, i.e., a revised Tsallis–Pareto-type function. The contribution of the two participant quarks to the transverse momentum distribution is then the convolution of two TP-like functions. The model distribution can be used to fit the experimental spectra measured by different collaborations. The related parameters such as the entropy index-related, effective temperature, and revised index are then obtained. The trends of these parameters are useful to understand the characteristic of high energy collisions.

We analyze the transverse momentum (pT) spectra of lepton pairs (ℓℓ¯) generated in the Drell-Yan process, as detected in proton-nucleus (pion-nucleus) and proton-(anti)proton collisions by ten collaborations over a center-of-mass energy sNN or s if in a simplified form) range from ~20 GeV to above 10 TeV. Three types of probability density functions (the convolution of two Lévy-Tsallis functions, the two-component Erlang distribution, and the convolution of two Hagedorn functions) are utilized to fit and analyze the pT spectra. The fit results are approximately in agreement with the collected experimental data. Consecutively, we obtained the variation law of related parameters as a function of s and invariant mass Q. In the fit procedure, a given Lévy-Tsallis (or Hagedorn) function can be regarded as the probability density function of transverse momenta contributed by a single quark (q) or anti-quark (q¯). The Drell-Yan process is then described by the statistical method.

Transverse momentum spectra of particles produced in high energy collisions are very important due to their relations to the excitation degree of interacting system. To describe the transverse momentum spectra, one can use more than one probability density functions of transverse momenta, which are simply called the functions or distributions of transverse momenta in some cases. In this paper, a few distributions of transverse momenta in high energy collisions are compared with each other in terms of plots to show some quantitative differences. Meanwhile, in the framework of Tsallis statistics, the distributions of momentum components, transverse momenta, rapidities, and pasudorapidities are obtained according to the analytical and Monte Carlo methods. These analyses are useful to understand carefully different distributions in high energy collisions. Keywords: Transverse momentum spectra, Different distributions, High energy collisions

Transverse momentum (mass) spectra of positively and negatively charged pions and of positively and negatively charged kaons, protons, and antiprotons produced at mid-(pseudo)rapidity in various collisions at high energies are analyzed in this work. The experimental data measured in central gold-gold, central lead-lead, and inelastic proton-proton collisions by several international collaborations are studied. The (two-component) standard distribution is used to fit the data and extract the excitation function of effective temperature. Then, the excitation functions of kinetic freeze-out temperature, transverse flow velocity, and initial temperature are obtained. In the considered collisions, the four parameters increase with the increase of collision energy in general, and the kinetic freeze-out temperature appears at the trend of saturation at the top Relativistic Heavy Ion Collider and the Large Hadron Collider.

The yield ratios of negatively to positively charged pions (π−/π+), negatively to positively charged kaons (K−/K+), and anti-protons to protons (p¯/p) produced in mid-rapidity interval in central gold-gold (Au-Au) collisions, central lead-lead (Pb-Pb) collisions, and inelastic (INEL) or non-single-diffractive (NSD) proton-proton (pp) collisions, as well as in forward rapidity region in INEL pp collisions are analyzed in the present work. Over an energy range from a few GeV to above 10 TeV, the chemical potentials of light flavor particles (pion, kaon, and proton) and quarks (up, down, and strange quarks) are extracted from the mentioned yield ratios in which the contributions of strong decay from high-mass resonance and weak decay from heavy flavor hadrons are removed. Most energy dependent chemical potentials show the maximum at about 4 GeV, while the energy dependent yield ratios do not show such an extremum.

The transverse momentum spectra of J/ψ, ψ2S, and YnS,n=1,2,3 produced in proton-proton p+p, proton-antiproton p+p¯, proton-lead p+Pb, gold-gold Au+Au, and lead-lead (Pb+Pb) collisions over a wide energy range are analyzed by the (two-component) Erlang distribution, the Hagedorn function (the inverse power-law), and the Tsallis-Levy function. The initial temperature is obtained from the color string percolation model from the fit by the (two-component) Erlang distribution in the framework of a multisource thermal model. The excitation functions of several parameters such as the mean transverse momentum and initial temperature increase from 39 GeV to 13 TeV, which is considered in this work. The mean transverse momentum and initial temperature decrease (increase slightly or do not change significantly) with the increase of rapidity (centrality). Meanwhile, the mean transverse momentum of YnS,n=1,2,3 is larger than that of J/ψ and ψ2S, and the initial temperature for YnS,n=1,2,3 emission is higher than that for J/ψ and ψ2S emission, which shows a mass-dependent behavior.

The transverse momentum spectra of identified particles produced in high energy proton-proton p+p collisions are empirically described by a new method with the framework of the participant quark model or the multisource model at the quark level, in which the source itself is exactly the participant quark. Each participant (constituent) quark contributes to the transverse momentum spectrum, which is described by the TP-like function, a revised Tsallis–Pareto-type function. The transverse momentum spectrum of the hadron is the convolution of two or more TP-like functions. For a lepton, the transverse momentum spectrum is the convolution of two TP-like functions due to two participant quarks, e.g., projectile and target quarks, taking part in the collisions. A discussed theoretical approach seems to describe the p+p collisions data at center-of-mass energy s=200 GeV, 2.76 TeV, and 13 TeV very well.

The momentum spectra of charged pions (π+ and π−) and kaons (K+ and K−), as well as protons (p), produced in the beam proton-induced collisions in a 90 cm long graphite target (proton-carbon (p-C) collisions) at the beam momentum pLab=31 GeV/c are studied in the framework of a multisource thermal model by using Boltzmann distribution and the Monte Carlo method. The theoretical model results are approximately in agreement with the experimental data measured by the NA61/SHINE Collaboration. The related free parameters (effective temperature, rapidity shifts, and fraction of nonleading protons) and derived quantities (average transverse momentum and initial quasitemperature) under given experimental conditions are obtained. The considered free parameters and derived quantities are shown to be strongly dependent on the emission angle over a range from 0 to 380 mrad and weakly dependent on longitudinal position (graphite target thickness) over a range from 0 to 90 cm.

Centrality-dependent double-differential transverse momentum spectra of negatively charged particles (π−, K−, and p¯) at the mid(pseudo)rapidity interval in nuclear collisions are analyzed by the standard distribution in terms of multicomponent. The experimental data measured in gold-gold (Au-Au) collisions by the PHENIX Collaboration at the Relativistic Heavy Ion Collider (RHIC) and in lead-lead (Pb-Pb) collisions by the ALICE Collaboration at the Large Hadron Collider (LHC) are studied. The effective temperature, initial temperature, kinetic freeze-out temperature, transverse flow velocity, and kinetic freeze-out volume are extracted from the fitting to transverse momentum spectra. We observed that the mentioned five quantities increase with the increase of event centrality due to the fact that the average transverse momentum increases with the increase of event centrality. This renders that larger momentum (energy) transfer and further multiple scattering had happened in central centrality.

The transverse momentum spectra of different types of particles, π±, K±, p and 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.

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.

The rapidity dependent transverse momentum spectra of heavy quarkonia (J/ψ and Υ mesons) produced in small collision systems such as proton-proton (pp) and proton-lead (p-Pb) collisions at center-of-mass energy (per nucleon pair) s (sNN) = 5-13 TeV are described by a two-component statistical model which is based on the Tsallis statistics and inverse power-law. The experimental data measured by the LHCb Collaboration at the Large Hadron Collider (LHC) are well fitted by the model results. The related parameters are obtained and the dependence of parameters on rapidity is analyzed.

The transverse momentum spectra of π-, π+, K-, K+, p¯, and p produced in Au+Au collisions at center-of-mass energy sNN=7.7, 11.5, 19.6, 27, 39, 62.4, 130, and 200 GeV are analyzed in the framework of a multisource thermal model. The experimental data measured at midrapidity by the STAR Collaboration are fitted by the (two-component) standard distribution. The effective temperature of emission source increases obviously with the increase of the particle mass and the collision energy. At different collision energies, the chemical potentials of up, down, and strange quarks are obtained from the antiparticle to particle yield ratios in given transverse momentum ranges available in experiments. With the increase of logarithmic collision energy, the chemical potentials of light flavor quarks decrease exponentially.

The experimental (simulated) transverse momentum spectra of negatively charged pions produced at midrapidity in central nucleus-nucleus collisions at the Heavy-Ion Synchrotron (SIS), Relativistic Heavy-Ion Collider (RHIC), and Large Hadron Collider (LHC) energies obtained by different collaborations are selected by us to investigate, where a few simulated data are taken from the results of FOPI Collaboration which uses the IQMD transport code based on Quantum Molecular Dynamics. A two-component standard distribution and the Tsallis form of standard distribution are used to fit these data in the framework of a multisource thermal model. The excitation functions of main parameters in the two distributions are analyzed. In particular, the effective temperatures extracted from the two-component standard distribution and the Tsallis form of standard distribution are obtained, and the relation between the two types of effective temperatures is studied.

The transverse momentum distributions of final-state particles are very important for high energy collision physics. In this work, we investigate J/ψ and Υ meson distributions in the framework of a particle-production source, where Tsallis statistics are consistently incorporated. The results are in good agreement with the experimental data in p-p and p-Pb collisions at LHC energies. The temperature of the emission source and the nonequilibrium degree of the collision system are extracted.

We study the transverse momentum spectra of J/ψ and Υ mesons by using two methods: the two-component Erlang distribution and the two-component Schwinger mechanism. The results obtained by the two methods are compared and found to be in agreement with the experimental data of proton-proton (pp), proton-lead (p-Pb), and lead-lead (Pb-Pb) collisions measured by the LHCb and ALICE Collaborations at the large hadron collider (LHC). The related parameters such as the mean transverse momentum contributed by each parton in the first (second) component in the two-component Erlang distribution and the string tension between two partons in the first (second) component in the two-component Schwinger mechanism are extracted.

Experimental results of the rapidity distributions of negatively charged pions produced in proton-proton (p-p) and beryllium-beryllium (Be-Be) collisions at different beam momentums, measured by the NA61/SHINE Collaboration at the super proton synchrotron (SPS), are described by a revised (three-source) Landau hydrodynamic model. The squared speed-of-sound parameter cs2 is then extracted from the width of rapidity distribution. There is a local minimum (knee point) which indicates a softest point in the equation of state (EoS) appearing at about 40A GeV/c (or 8.8 GeV) in cs2 excitation function (the dependence of cs2 on incident beam momentum (or center-of-mass energy)). This knee point should be related to the searching for the onset of quark deconfinement and the critical point of quark-gluon plasma (QGP) phase transition.

Transverse momentum (pT) and rapidity (y) spectra of Z bosons and quarkonium states (some charmonium cc¯ mesons such as J/ψ and ψ(2S) and some bottomonium bb¯ mesons such as Υ(1S), Υ(2S), and Υ(3S)) produced in proton-proton (pp) and lead-lead (Pb-Pb) collisions at the large hadron collider (LHC) are uniformly described by a hybrid model of two-component Erlang distribution for pT spectrum and two-component Gaussian distribution for y spectrum. The former distribution results from a multisource thermal model, and the latter one results from the revised Landau hydrodynamic model. The modelling results are in agreement with the experimental data measured in pp collisions at center-of-mass energies s=2.76 and 7 TeV and in Pb-Pb collisions at center-of-mass energy per nucleon pair sNN=2.76 TeV. Based on the parameter values extracted from pT and y spectra, the event patterns (particle scatter plots) in two-dimensional pT-y space and in three-dimensional velocity space are obtained.

We present two methods to extract the chemical potentials of quarks in high energy collisions. The first method is based on the ratios of negatively/positively charged particles, and the temperatures extracted from the transverse momentum spectra of related hadrons are needed. The second method is based on the chemical potentials of some particles, and we also need the transverse momentum spectra of related hadrons. To extract the quark chemical potentials, we would like to propose experimental collaborations to measure simultaneously not only the transverse momentum spectra of p-, p, K-, K+, π-, and π+, but also those of D-, D+, B-, and B+ (even those of Δ++, Δ-, and Ω-) in high energy nuclear collisions.

In Tsallis statistics, we investigate charged pion and proton production for pCu and pPb interactions at 3, 8, and 15 GeV/c. Two versions of Tsallis distribution are implemented in a multisource thermal model. A comparison with experimental data of the HARP-CDP group shows that they both can reproduce the transverse momentum spectra, but the improved form gives a better description. It is also found that the difference between q and q′ is small when the temperature T = T′ for the same incident momentum and angular interval, and the value of q is greater than q′ in most cases.

The transverse momentum distributions of jets produced in p-p, p-p-, d-Au, Au-Au, and Pb-Pb collisions at high energies with different selected conditions are analyzed by using a multisource thermal model. The multicomponent (mostly two-component) Erlang distribution used in our description is in good agreement with the experimental data measured by the STAR, D0, CDF II, ALICE, ATLAS, and CMS Collaborations. Related parameters are extracted from the transverse momentum distributions and some information on different interacting systems is obtained. In the two-component Erlang distribution, the first component has usually two or more sources which are contributed by strong scattering interactions between two quarks or more quarks and gluons, while the second component has mostly two sources which are contributed by harder head-on scattering between two quarks.

We propose a new revised Landau hydrodynamic model to study systematically the pseudorapidity distributions of charged particles produced in heavy ion collisions over an energy range from a few GeV to a few TeV per nucleon pair. The interacting system is divided into three sources, namely, the central, target, and projectile sources, respectively. The large central source is described by the Landau hydrodynamic model and further revised by the contributions of the small target/projectile sources. The modeling results are in agreement with the available experimental data at relativistic heavy ion collider, large hadron collider, and other energies for different centralities. The value of square speed of sound parameter in different collisions has been extracted by us from the widths of rapidity distributions. Our results show that, in heavy ion collisions at energies of the two colliders, the central source undergoes a phase transition from hadronic gas to quark-gluon plasma liquid phase; meanwhile, the target/projectile sources remain in the state of hadronic gas. The present work confirms that the quark-gluon plasma is of liquid type rather than being of a gas type.

The transverse momentum and rapidity distributions of net-baryons (baryons minus antibaryons) produced in central gold-gold (Au-Au) collisions at 62.4 and 200 GeV are analyzed in the framework of a multisource thermal model. Each source in the model is described by the Tsallis statistics to extract the effective temperature and entropy index from the transverse momentum distribution. The two parameters are used as input to describe the rapidity distribution and to extract the rapidity shift and contribution ratio. Then, the four types of parameters are used to structure some scatter plots of the considered particles in some three-dimensional (3D) spaces at the stage of kinetic freeze-out, which are expected to show different characteristics for different particles and processes. The related methodology can be used in the analyses of particle production and event holography, which are useful for us to better understand the interacting mechanisms.

The revised (three-source) Landau hydrodynamic model is used in this paper to study the (pseudo)rapidity distributions of charged particles produced in proton-proton and proton-antiproton collisions at high energies. The central source is assumed to contribute with a Gaussian function which covers the rapidity distribution region as wide as possible. The target and projectile sources are assumed to emit isotropically particles in their respective rest frames. The model calculations obtained with a Monte Carlo method are fitted to the experimental data over an energy range from 0.2 to 13 TeV. The values of the squared speed-of-sound parameter in different collisions are then extracted from the width of the rapidity distributions.

Two-particle azimuthal correlations are studied in the framework of a multisource thermal model. Each source is assumed to produce many particles. Each particle pair measured in final state is considered to be produced at two emission points (subsources) in a single or two sources. The first emission point corresponds to the production of “trigger” particle and the second one corresponds to that of “associated” particle. There are oscillations and other interactions between the two emission points. In the rest frame of the “associated” particle's emission point, the oscillations and other interactions cause the momentum of the “trigger” particle to depart from the original value. The modelling results are in agreement with the experimental data of proton-lead (p-Pb) collisions at sNN = 5.02 TeV, one of the Large Hadron Collider energies, measured by the ALICE and ATLAS Collaborations.

Pseudorapidity distributions of charged particles produced in proton-proton (p-p) or proton-antiproton (p-p-) collisions over an energy range from 0.053 to 7 TeV are studied by using the four-component Landau hydrodynamic model. The results calculated by the model are in agreement with the experimental data of the UA5, PHOBOS, UA1, P238, CDF, ALICE, and CMS Collaborations which present orderly from low to high energies. According to the distribution widths of different components, the values and some features of square speed of sound parameter cs2 for “participant” and “spectator” quark components are obtained. It is shown that the speed of sound for “participant” quark components agrees approximately with that for “spectator” quark components in the error ranges. The present work is useful for studying nucleus-nucleus collisions in the related energy range.

Based on the (pseudo)rapidity distribution of final-state particles produced in proton-proton (pp) collisions at high energy, the probability distributions of momenta, longitudinal momenta, transverse momenta (transverse masses), energies, velocities, longitudinal velocities, transverse velocities, and emission angles of the considered particles are obtained in the framework of a multisource thermal model. The number density distributions of particles in coordinate and momentum spaces and related transverse planes, the particle dispersion plots in longitudinal and transverse coordinate spaces, and the particle dispersion plots in transverse momentum plane at the stage of freeze out in high energy pp collisions are also obtained.

The transverse momentum spectrums of final-state products produced in nucleus-nucleus and proton-proton collisions at different center-of-mass energies are analyzed by using a multicomponent Erlang distribution and the Lévy distribution. The results calculated by the two models are found in most cases to be in agreement with experimental data from the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). The multicomponent Erlang distribution that resulted from a multisource thermal model seems to give a better description as compared with the Lévy distribution. The temperature parameters of interacting system corresponding to different types of final-state products are obtained. Light particles correspond to a low temperature emission, and heavy particles correspond to a high temperature emission. Extracted temperature from central collisions is higher than that from peripheral collisions.

The transverse momentum and pseudorapidity distributions of charged particles produced in Pb-Pb collisions with different centrality intervals at center-of-mass energy per nucleon pair sNN=2.76 TeV have been analyzed by using the improved multisource thermal model in which the whole interacting system and then the sources are described by the Tsallis statistics. The modelling results are in agreement with experimental data of the ALICE Collaboration. The rapidity distributions of charged particles are obtained according to the extracted parameter values. The shapes of interacting events (the dispersion plots of charged particles) are given in the momentum, rapidity, velocity, and coordinate spaces. Meanwhile, the event shapes in different spaces consisted by different transverse quantities and longitudinal quantities are presented.

The double-differential π± production cross sections in interactions of charged pions on targets at high momentums are analyzed by using a multicomponent Erlang distribution which is obtained in the framework of a multisource thermal model. The calculated results are compared and found to be in agreement with the experimental data at the incident momentums of 3, 5, 8, and 12 GeV/c measured by the HARP Collaboration. It is found that the source contributions to the mean momentum of charged particles and to the distribution width of particle momentums decrease with increase of the emission angle, and the source number and temperature do not show an obvious dependence on the emission angle of the considered particle.

In the framework of a multisource thermal model, the transverse momentum distributions of charged particles produced in nucleus-nucleus (A-A) and deuteron-nucleus (d-A) collisions at relativistic heavy ion collider (RHIC) energies are investigated by a two-component revised Boltzmann distribution. The calculated results are in agreement with the PHENIX experimental data. It is found that the source temperature increases obviously with increase of the particle mass and incident energy, but it does not show an obvious change with the collision centrality. Then, the values of chemical potentials for up, down, and strange quarks can be obtained from the antiparticle to particle yield ratios in a wide transverse momentum range. The relationship between the chemical potentials of quarks and the transverse momentum with different centralities is investigated, too.

The transverse momentum spectra obtained in the frame of an isotropic emission source are compared in terms of Tsallis, Boltzmann, Fermi-Dirac, and Bose-Einstein distributions and the Tsallis forms of the latter three standard distributions. It is obtained that, at a given set of parameters, the standard distributions show a narrower shape than their Tsallis forms which result in wide and/or multicomponent spectra with the Tsallis distribution in between. A comparison among the temperatures obtained from the distributions is made with a possible relation to the Boltzmann temperature. An example of the angular distributions of projectile fragments in nuclear collisions is given.

In framework of combing the participant-spectator model and the Landau hydrodynamic model, the pseudorapidity distributions of charged particles produced in heavy-ion (or nucleus-nucleus) collisions at RHIC and LHC energies are described by a modified Landau hydrodynamic model, where the Landau hydrodynamic model is applied to the target/projectile spectators and the target/projectile participants, respectively. The modeling results are in agreement with the PHOBOS and ALICE experimental data. Then, the values of square speed of sound (cs2) for the participants and spectators can be obtained from the widths of charged particle pseudorapidity distributions. Some features of cs2 for different centralities and center-of-mass energies are obtained too.

The multisource thermal model is used in this paper to analyze the antiproton (p¯) production process in high-energy proton-carbon (p-C) collisions. The transverse momentum, Feynman variable, and rapidity distributions of antiprotons in the nucleon-nucleon center-of-mass system are calculated by using the model. The modeling results are compared and found to be in agreement with the experimental data measured by the NA49 Collaboration at 158 GeV/c beam momentum. As a parameter, the nuclear temperature of interacting system extracted from the antiproton spectrum is estimated to be about 150 MeV.

The inclusive particle productions in proton-proton (pp) and deuton-gold (d+Au) collisions at forward rapidity at the Relativistic Heavy Ion Collider (RHIC) energy are studied in the framework of the color glass condensate (CGC) theory by using two different initial conditions: AAMQS (Albacete-Armesto-Milhano-Quiroga-Salgado) and quartic action. Then, the results obtained by the two different initial conditions in illustrating the effect of valence color charges in high-energy proton-nucleus (pA) collisions at forward energy are compared. Meanwhile, the inclusive particle productions in pA collisions at forward rapidity at the Large Hadron Collider (LHC) energies are predicted. The main dynamical input in our calculations is the use of solutions of the running coupling Balitsky-Kovchegov equation tested in electron-proton (ep) collision data. Particle production is computed via the hybrid formalisms to obtain spectra and yields. These baseline predictions are useful for testing the current understanding of the dynamics of very strong color fields against the upcoming LHC data.

In high energy collisions, one usually needs to give a conversion between the particle rapidity and pseudorapidity distributions. Currently, two equivalent conversion formulas are used in experimental and theoretical analyses. An investigation in the present work shows that the two conversions are incomplete. Then, we give a revision on the current conversion between the particle rapidity and pseudorapidity distributions.