Initial- and final-state temperatures of emission source from differential cross-section in squared momentum transfer in high energy collisions

The differential cross-section in squared momentum transfer of $\rho$, $\rho^0$, $\omega$, $\phi$, $f_{0}(980)$, $f_{1}(1285)$, $f_{0}(1370)$, $f_{1}(1420)$, $f_{0}(1500)$, and $J/\psi$ produced in high energy virtual photon-proton ($\gamma$$^{*} p$), photon-proton ($\gamma p$), and proton-proton ($pp$) collisions measured by the H1, ZEUS, and WA102 Collaborations are 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 higher one, and decrease with increasing of center-of-mass energy.