Analytical Results for the Classical and Quantum Tsallis Hadron Transverse Momentum Spectra: the Zeroth Order Approximation and beyond

We derive the analytical expressions for the first and second order terms in the hadronic transverse momentum spectra obtained from the Tsallis normalized (Tsallis-1) statistics. We revisit the zeroth order quantum Tsallis distributions and obtain the corresponding analytical closed form expressions. It is observed that unlike the classical case, the analytical closed forms of the zeroth order quantum spectra do not resemble the phenomenological distributions used in the literature after $q \to q^{-1}$ substitution, where $q$ is the Tsallis entropic parameter. However, the factorization approximation increases the extent of similarity.