Disentangling random thermal motion of particles and collective expansion of source from transverse momentum spectra in high energy collisions

Abstract: In the framework of a multisource thermal model, we describe experimental results of the transverse momentum spectra of final-state light flavour particles produced in gold-gold (Au-Au), copper-copper (Cu-Cu), lead-lead (Pb-Pb), proton-lead ($p$-Pb), and proton-proton ($p$-$p$) collisions at various energies, measured by the PHENIX, STAR, ALICE, and CMS Collaborations, by using the Tsallis-standard (Tsallis form of Fermi-Dirac or Bose-Einstein), Tsallis, and two- or three-component standard distributions which can be in fact regarded as different types of "thermometers" or "thermometric scales" and "speedometers". A central parameter in the three distributions is the effective temperature which contains information on the kinetic freeze-out temperature of the emitting source and reflects the effects of random thermal motion of particles as well as collective expansion of the source. To disentangle both effects, we extract the kinetic freeze-out temperature from the intercept of the effective temperature ($T$) curve as a function of particle's rest mass ($m_0$) when plotting $T$ versus $m_0$, and the mean transverse flow velocity from the slope of the mean transverse momentum ($\langle p_T \rangle$) curve as a function of mean moving mass ($\overline{m}$) when plotting $\langle p_T \rangle$ versus $\overline{m}$.