c_{\alpha}\left(  \frac{W}{Q_{0}}\right)  ^{\lambda
/(2+\lambda)}+2b_{\alpha}\frac{m_{\alpha}}{Q_{0}}\right)\end{aligned}$$ with$$c_{a}=\frac{1}{2+\lambda}%
%TCIMACRO{\dint }%
%BeginExpansion
{\displaystyle\int}
%EndExpansion
F_{\alpha}(\tau)\tau^{-(\lambda-1)/(2+\lambda)}d\tau.\label{calpha}%$$ Hence mean $p_{\text{T}}$ reads$$\left\langle p_{\text{T}}\right\rangle =Q_{0}\frac{c_{\alpha}\left(  \frac
{W}{Q_{0}}\right)  ^{\lambda/(2+\lambda)}+2b_{\alpha}\frac{m_{\alpha}}{Q_{0}}%
}{b_{\alpha}+a_{\alpha}\frac{m_{\alpha}}{Q_{0}}\left(  \frac{W}{Q_{0}}\right)
^{-\lambda/(2+\lambda)}}\simeq Q_{0}\frac{c_{\alpha}}{b_{\alpha}}\left(
\frac{W}{Q_{0}}\right)  ^{\lambda/(2+\lambda)}+m_{\alpha}\left(
2-\frac{a_{\alpha}c_{\alpha}}{b_{\alpha}^{2}}\right)  .\label{meanpt1}%$$ We see that mean transverse momentum behaves as a constant (proportional to the particle mass) plus a power of energy, which is also confirmed by the recent data up to the LHC energies [@:2009dt]. Let us remark that formulae (\[dNdy\]) and (\[meanpt1\]) imply in the leading order $$\left\langle p_{\text{T}}\right\rangle =A+B\sqrt{dN/dy}.$$

Universal shape of geometrical scaling and Tsallis-like parametrization {#shape}
=======================================================================

We shall now be more specific and use a particular form of function $F_{\alpha}(\tau)$. This will allow us to calculate explicitly constants $a_{\alpha
},b_{\beta}$ and $c_{\alpha}$. To this end we shall use the experimental observation that identified particles spectra can be well described in terms of Tsallis-like parametrization of Eq. (\[Tsallis\]) with species dependent temperature $T=T_{\alpha}$ and exponent $n=n_{\alpha}$. In actual fits to the data $n_{\alpha}$ is of the order $5$ to 9 [@Chatrchyan:2012qb], therefore we may use an approximation$$C_{\alpha}\simeq\frac{\gamma_{\alpha} }{T_{\alpha}^{2}}\label{Cappr}%$$ where constant $\gamma_{\alpha} $ restores the correct normalization being only a function of $n_{\alpha}$. Inserting (\[Cappr\]) and (\[change\]) into (\[Tsallis\]) we obtain:$$\frac{d^{2}N_{\alpha}}{dydp_{\text{T}}^{2}}=\frac{\gamma_{\alpha} }
{2T_{\alpha}^{2}}\frac{dN_{\alpha}}{dy}\left[  1+\frac{Q_{0}\left(  \frac
{W}{Q_{0}}\right)  ^{\lambda/(2+\lambda)}\tau^{1/(2+\lambda)}}{n_{\alpha
}\,T_{\alpha}}\right]  ^{-n_{\alpha}}.$$ Finally, 