had chosen $p_{\mathrm{T}}$ as an argument in the saturation scale leading to scaling variable $\tau_{\tilde{m}_{\mathrm{T}%
}p_{\mathrm{T}}}$ (\[taumtpdef\]), so called $\tilde{m}_{\mathrm{T}}%
$$p_{\mathrm{T}}$ – scaling. This is illustrated in Fig. \[ratiosmandpT\].a – \[ratiosmandpT\].c where full symbols refer to the $p_{\mathrm{T}}$ – scaling (\[taupdef\]) and open symbols to $\tilde{m}_{\mathrm{T}}$ – scaling or $\tilde{m}_{\mathrm{T}}$$p_{\mathrm{T}}$ – scaling. One can see very small difference between open symbols indicating that scaling variables $\tau_{\tilde{m}_{\mathrm{T}}}$ (\[taumtdef\]) and $\tau_{\tilde
{m}_{\mathrm{T}}p_{\mathrm{T}}}$ (\[taumtpdef\]) exhibit GS of the same quality. On the contrary $p_{\mathrm{T}}$ – scaling in variable $\tau_{p_{\rm T}}$ (\[taupdef\]) is visibly worse than any form of scaling variable involving $\tilde{m}_{\mathrm{T}}$.

Finally in Fig. \[ratiosmandpT\].d, on the example of protons, we compare $\tilde{m}_{\mathrm{T}}$ – scaling and ${m}_{\mathrm{T}}$ – scaling for $\lambda=0.27$. One can see that no GS has been achieved in the latter case. Qualitatively the same behavior can be observed for other values of $\lambda$.

![Panels a) – c): comparison of geometrical scaling in three different variables: $\tau_{p_{\rm T}}$, $\tau_{\tilde{m}_{\rm T}}$ and $\tau_{\tilde{m}_{\rm T} p_{\rm T}}$ for $\lambda=0.27$. Full symbols correspond to ratios $R_{W_{1}/W_{2}}$ plotted in terms of the scaling variable $\tau_{p_{\rm T}}$, open symbols to $\tau_{\tilde{m}_{\rm T}}$ and $\tau_{\tilde{m}_{\rm T}%
p_{\rm T}}$, note negligible differences between the latter two forms 