Multiplicity dependence of the freezeout parameters in high energy hadron-hadron collisions

We examined the transverse momentum（pT） spectra of various identified particles,encompassing both light-flavored and strange hadrons（π+π-,K++K-,■）,across different multiplicity classes in proton-proton collisions（p-p） at a center-of-mass energy of S1/2=7 TeV.Utilizing the Tsallis and Hagedorn models,parameters relevant to the bulk properties of nuclear matter were extracted.Both models exhibit good agreement with experimental data.In our analyses,we observed a consistent decrease in the effective temperature（T） for the Tsallis model and the kinetic or thermal freeze-out temperature（T0） for the Hagedorn model,as we transitioned from higher multiplicity（class-I） to lower multiplicity（class-X）.This trend is attributed to the diminished energy transfer in higher multiplicity classes.Additionally,we observed that the transverse flow velocity experiences a decline from class-I to class-X.The normalization constant,which represents the multiplicity of produced particles,was observed to decrease as we moved toward higher multiplicity classes.While the effective and kinetic freeze-out temperatures,as well as the transverse flow velocity,show a mild dependency on multiplicity for lighter particles,this dependency becomes more pronounced for heavier particles.The multiplicity parameter for heavier particles was observed to be smaller than that of lighter particles,indicating a greater abundance of lighter hadrons compared to heavier ones.Various particle species were observed to undergo decoupling from the fireball at distinct temperatures:lighter particles exhibit lower temperatures,while heavier ones show higher temperatures,thereby supporting the concept of multiple freeze-out scenarios.Moreover,we identified a positive correlation between the kinetic freeze-out temperature and transverse flow velocity,a scenario where particles experience stronger collective motion at a higher freeze-out temperature.The reason for this positive correlation is that,as the multiplicity increases,more energy is transferred into the system.This increased energy causes greater excitation and pressure within the system,leading to a quick expansion.