(n_{\alpha}\,\kappa_{\alpha})^{2}B(2,n_{\alpha}-2),\nonumber\\
c_{\alpha}  & =\frac{\gamma_{\alpha}b_{\alpha}}{2 \kappa_{\alpha}^{2}}%
(n_{\alpha}\,\kappa_{\alpha})^{3}B(3,n_{\alpha}-3)\label{abc}%\end{aligned}$$ where $B(x,y)$ is Euler beta function. The second equation (\[abc\]) should be understood as a normalization condition for $\gamma_{\alpha}$:$$\gamma_{\alpha}=\frac{2}{n_{\alpha}^{2}\,B(2,n_{\alpha}-2)}%$$ which is independent of $\kappa_{\alpha}$, as expected. With this normalization we arrive at: $$a_{\alpha}=\frac{b_{\alpha}}{\kappa_{\alpha}} \frac{n_{\alpha}-2}{n_{\alpha}%
},\;\;\;\; c_{\alpha}={b_{\alpha}}{\kappa_{\alpha}} \frac{2 n_{\alpha}%
}{n_{\alpha}-3}%$$ with $b_{\alpha}$ being a free constant which can be fitted from the energy dependence of the mid rapidity density (\[dNdy\]). The coefficient governing the constant piece in a formula for $\left\langle
p_{\text{T}}\right\rangle $ (\[meanpt1\]) is given by:$$\begin{aligned}
2-\frac{a_{\alpha}c_{\alpha}}{b_{\alpha}^{2}}  & =-\frac{2}{n_{\alpha}%
-3}.\label{coeffpt}%\end{aligned}$$ It is important to note that this coefficient is negative for values of $n_{\alpha}$ extracted from the data [@Chatrchyan:2012qb] and that the constant piece in Eq. (\[meanpt1\]) is growing with particle mass. Note, however, that there might exist a nonperturbative contribution to this term which is beyond control in the present approach.

Conclusions {#concl}
===========

In this paper we have demonstrated using recent ALICE pp data for identified particles at three LHC energies [@ALICE] that transverse momentum spectra exhibit geometrical scaling in variable $\tau_{\tilde{m}_{\rm T}}=
(\tilde{m}_{\rm T}/Q_0)^{2} (\tilde{m}_{\rm T}/ W)^{\lambda}$. It is impossible at present to asses quantitatively the quality of this scaling, since the data for $W=0.9$ and $2.76$ TeV published so far, 