We derive 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 in this formulation and obtain the corresponding analytical closed form expressions. It is observed that unlike the classical case, the phenomenological distributions used in the literature do not resemble the analytical closed forms of the zeroth order quantum spectra after the \(q\rightarrow q^{-1}\) substitution, where q is the Tsallis entropic parameter. Though the factorization approximation increases the extent of similarity, it does not make them exactly the same. Since our results are based on the basic formulations of the statistical mechanics, the zeroth order Tsallis quantum distributions derived in this paper will be a better choice than their phenomenological counterparts.

我们推导出从 Tsallis 归一化 (Tsallis-1) 统计数据获得的强子横向动量谱中的一阶和二阶项的解析表达式。我们重新审视这个公式中的零阶量子 Tsallis 分布，并获得相应的解析闭式表达式。据观察，与经典情况不同，文献中使用的现象学分布与\(q\rightarrow q^{-1}\)置换后的零阶量子谱的解析闭合形式并不相似，其中q是 Tsallis 熵参数。尽管分解近似增加了相似程度，但并没有使它们完全相同。由于我们的结果基于统计力学的基本公式，因此本文中推导出的零阶 Tsallis 量子分布将是比现象学对应物更好的选择。