A thermal model, based on the Tsallis distribution and blast-wave model, is proposed to compute hadron double-differential spectra d(2)N/dp(T)dy in pp (also high-energy p (p) over bar) collisions. It successfully describes the available experimental data on pion and quarkonia [phi, J/psi, psi(2S), (sic) family] production at energies from root s = 5 GeV to the LHC ones. Simple parametrizations for the root s dependence of the model parameters are provided, allowing predictions for the yields of these particles at new collision energies. The model can be used also for the pion Bose-Einstein correlation studies.
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