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Initial, effective, and kinetic freeze-out temperatures from transverse momentum spectra in high energy proton(deuteron)-nucleus and nucleus-nucleus collisions

The transverse momentum spectra of charged particles produced in proton(deuteron)-nucleus and nucleus-nucleus collisions at high energies are analyzed by the Hagedorn thermal model and the standard distribution in terms of multi-component. The experimental data measured in central and peripheral gold-gold (Au-Au) and deuteron-gold ($d$-Au) collisions by the PHENIX Collaboration at the Relativistic Heavy Ion Collider (RHIC), as well as in central and peripheral lead-lead (Pb-Pb) and proton-lead ($p$-Pb) collisions by the ALICE Collaboration at the Large Hadron Collider (LHC) are fitted by the two models. The initial, effective, and kinetic freeze-out temperatures are then extracted from the fitting to the transverse momentum spectra. It is shown that the initial temperature is larger than the effective temperature, and the effective temperature is larger than the kinetic freeze-out temperature. The three types of temperatures in central collisions are comparable with those in peripheral collisions, and those at the LHC are comparable with those at the RHIC.