particle masses provide yet another external energy scale that might lead to GS violation [@Stebel:2013kca]. It is the purpose of the present paper to see whether this is really the case.

It is well known that particle spectra at low and medium transverse momenta can be described by thermal distributions in transverse mass $m_{\mathrm{T}%
}=\sqrt{p^{2}_{\mathrm{T}}+m^{2}}$ with “temperature” $T$ which is a function of the scattering energy [@Hagedorn]. One may therefore hope that in some limited range geometrical scaling can be still present with pertinent scaling variable being $m^{2}_{\mathrm{T}}/Q^{2}_{\mathrm{s}}$. It is also known that more accurate fits are obtained by means of Tsallis-like parametrization [@Tsallis] where particle multiplicity distribution takes the following form (see *e.g.* [@Chatrchyan:2012qb]): $$\frac{1}{p_{\text{T}}}\frac{d^{2}N}{dydp_{\text{T}}}=C\frac{dN}{dy}\left[
1+\frac{m_{\mathrm{T}}-m}{n\,T}\right]  ^{-n}\label{Tsallis}%$$ with$$C=\frac{(n-1)(n-2)}{n\,T\left(  n\,T+(n-2)m\right)  }.\label{normC}%$$ Coefficient $C$ in Eq. (\[normC\]) ensures proper normalization of (\[Tsallis\]). Here $n$ and $T$ are free fit parameters that depend on particle species. In the limit $n \rightarrow\infty$ distribution (\[Tsallis\]) tends to the exponent $\exp(-m_{\mathrm{T}}/T)$, *i.e.* to the thermal distribution mentioned above. Formula (\[Tsallis\]) suggests yet another possibility of scaling variable, namely $\tilde{m}^{2}%
_{\mathrm{T}}/Q^{2}_{\mathrm{s}}$ where $$\tilde{m}_{\mathrm{T}}=m_{\mathrm{T}}-m=\sqrt{p^{2}_{\mathrm{T}}+m^{2}}-m
.\label{tildemT}%$$ Subtracting $m$ from $m_{\mathrm{T}}$ in (\[tildemT\]) contributes in the large $n$ limit to an overall factor and does not influence the functional 