Excitation functions of related temperatures of {\eta} and {\eta}0 emission sources from squared momentum transfer spectra in high-energy collisions

The squared momentum transfer spectra of $\eta$ and $\eta ^0$, produced in high-energy photon-proton ($\gamma p$) $\rightarrow {\rm meson + proton}$ process in electron-proton ($ep$) collisions performed at CEBAF, NINA, CEA, SLAC, DESY, and WLS are analyzed. The Monte Carlo calculations are used in the analysis of the squared momentum transfer spectra, where the transfer undergoes from the incident $\gamma$ to emitted meson or equivalently from the target proton to emitted proton. In the calculations, the Erlang distribution and Tsallis-Levy function are used to describe the transverse momentum spectra of emitted particles. Our results show that the average transverse momentum ($\langle p_T\rangle$), the initial-state temperature ($T_i$), and the final-state temperature ($T_0$) roughly decrease from lower center-of-mass energy ($W$) to higher one, and at several special $W$, this tendency is broken.