Excitation Function Of Related Parameters From Transverse Momentum(Mass) Spectra In High-Energy Collisions

The initial state,chemical freeze-out,and kinetic freeze-out are three main stages undergone by the interacting system in particle-particle,particle-nucleus,and nucleus-nucleus collisions at high energies.As the basic process,proton-proton collisions display some similarities to proton-nucleus and nucleus-nucleus collisions.In particular,proton-proton collisions and gold-gold(copper-copper,lead-lead,etc.)collisions have been studied in large-scale experiments at the Heavy Ion Synchrotron(SIS),Alternating Gradient Synchrotrin(AGS),Super Proton Synchrotron(SPS),Relativistic Heavy Ion Collider(RHIC),and Large Hadron Collider(LHC).A few productive collaborations have been reporting abundant data on the particle ratios,(pseudo)rapidity spectra,transverse momentum(mass)spectra,invariant mass spectra,anisotropic flows,nuclear modification factor,and so on.Some useful information related to particle production and system evolution can be extracted from these data.In order to extract the kinetic freeze-out temperature and transverse flow velocity and to study their dependence on energy,one can use different models to analyze the transverse momentum spectra.These models include,but are not limited to,the blast-wave model with Boltzmann-Gibbs statistics or with Tsallis statistics and the intercept-slope method with standard or Tsallis distribution,where the standard distribution denotes the Boltzmann,Fermi-Dirac,and Bose-Einstein distributions.The blast-wave model can obtain simultaneously the kinetic freeze-out temperature and transverse flow velocity from a single formula.The intercept-slope method needs a few steps to obtain the two quantities,where the intercept in the linear relation of effective temperature against rest mass is regarded as the kinetic freeze-out temperature,and the slope in the linear relation of mean transverse momentum against mean moving mass(mean energy)is regarded as the transverse flow velocity.The effective temperature is in fact the temperature parameter in the standard distribution in which the contribution of flow effect is not excluded.Comparatively,the blast-wave model is more convenient than the intercept-slope method.Transverse momentum spectra of negative and positive pions produced at mid-(pseudo)rapidity in inelastic or non-single-differactive 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 good agreement with the experimental data measured by a few productive collaborations worked at the SIS,SPS,RHIC,and LHC,respectively.The energy dependent kinetic freeze-out temperature and transverse flow velocity are obtained and analyzed.Both the quantities have a quick increase from the SIS to SPS,and slight increase or approximate invariability from the top RHIC to LHC.From the SPS to RHIC,the considered quantities in proton-proton collisions obtained by the blast-wave model with Boltzmann-Gibbs statistics show a more complex energy dependent behavior compared with the other three cases.In a particular superposition with Hagedorn function,both the excitation functions of kinetic freeze-out temperature(T0)of emission source and transverse flow velocity(?T)of produced particles obtained from a given selection in the blast-wave fit with Boltzmann distribution have a hill at(?)?10GeV,a drop at dozens of GeV,and then an increase from dozens of GeV to above 10 TeV.However,both the excitation functions of T0 and ?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,T0 and ?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.Transverse momentum(mass)spectra of charged pions,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 transverse momentum spectra of charged pions,kaons,and protons produced at mid-rapidity in central nucleus-nucleus collisions at high energies are analyzed by considering the contributions of two participant partons.Each participant 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 nucleus-nucleus 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 sidestep from near 10 GeV to 200 GeV in the excitation function of kinetic freeze-out temperature.