dependence of thermal distribution. For finite $n$, as we shall see, it has a significant impact on the shape of the multiplicity distribution. Moreover, variable $\tilde{m}_{\mathrm{T}}$ is “more similar” to $p_{\mathrm{T}}$ as it vanishes for $p_{\mathrm{T}} \rightarrow0$ for all particle species, while $m_{\mathrm{T}}$ goes to the species dependent threshold value $m_{\alpha}$. For large transverse momenta both $\tilde{m}_{\mathrm{T}}$ and $m_{\mathrm{T}}$ tend to $p_{\mathrm{T}}$.

Saturation scale $Q_{\mathrm{s}}$ characterizes small Bjorken $x$ gluon cloud developed in the colliding hadrons due to the BFKL-like evolution. It depends upon gluons’ $x$’s which for elastic scattering of massless gluons are given by $$x=\frac{p_{\mathrm{T}}}{\sqrt{s}}\,e^{\pm y}\label{Bjx}%$$ where $W=\sqrt{s}$ denotes c.m.s. scattering energy, $p_{\mathrm{T}}$ and $\pm
y$ refer to the transverse momentum and to the rapidities of scattered gluons. Saturation scale used originally in Refs. [@Stasto:2000er; @GolecBiernat:1998js] takes the following form $$Q_{\mathrm{s}}^{2} = Q_{0}^{2} \left(  \frac{x}{x_{0}}\right) ^{-\lambda
}\label{Qsdef}%$$ where $x_{0}$ is of the order of $10^{-3} - 10^{-4}$. Throughout this paper we shall assume $x_{0} =10^{-3} $. Our results, however, are not sensitive neither to this choice nor to the value of $Q_{0}$ for which we take 1 GeV/$c$. It follows from Eq. (\[Bjx\]) that in the case of (unidentified) charged particles spectra, scaling variable is naturally given as 