draw conclusions on GS in this case may lead to an underestimate of exponent $\lambda$ [@sikler2].

The examples presented in this Section illustrate that for identified particles geometrical scaling of good quality is observed for scaling variable (\[taumtdef\]) within the window $0.5 <\sqrt{\tau_{\tilde{m}_{\rm T}}} < 6$ for kaons and protons with lower bound shifted to 1.5 for pions. In the next Section we are going to investigate the consequences of this observation as far as the universal shape of scaling function $F_{\alpha}(\tau)$ is concerned.

Consequences of geometrical scaling {#conseq}
===================================

In what follows we shall assume that scaling variable $\tau=\tau_{\tilde
{m}_{\mathrm{T}}}$. We shall also suppress for the moment index $\alpha$ referring to the particle species. Let us first examine the energy dependence of mid rapidity multiplicity density and of average transverse momentum of produced particles. Following Eq. (\[GS\]), mid rapidity density is given by an integral $$\frac{dN}{dy}=\frac{1}{2\,Q_{0}^{2}}\int F(\tau) \,dp^{2}_{\text{T}%
}\label{GSint}%$$ which requires change of variables:$$dp_{\text{T}}^{2}=2(\tilde{m}_{\text{T}}+m_{\alpha})\,d\tilde{m}_{\text{T}}%$$ with$$\begin{aligned}
d\tilde{m}_{\text{T}}  & =\frac{Q_{0}}{2+\lambda}\left(  \frac{W}{Q_{0}%
}\right)  ^{\lambda/(2+\lambda)}\tau^{1/(2+\lambda)}\frac{d\tau}{\tau
}.\label{change}%\end{aligned}$$ Using (\[change\]) we arrive at (restoring dependence on particle species $\alpha$) $$\begin{aligned}
\frac{dN_{\alpha}}{dy}  & =b_{\alpha}\left(  \frac{W}{Q_{0}}\right)
^{2\lambda/(2+\lambda)}\left[  1+\frac{a_{\alpha}}{b_{\alpha}}\frac{m_{\alpha
}}{Q_{0}}\left(  \frac{W}{Q_{0}}\right)  ^{-\lambda/(2+\lambda)}\right]
.\label{dNdy}%\end{aligned}$$ We see therefore that mid rapidity identified particle density contains a universal leading term and 