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Based on the recent RHIC and LHC experimental results, the $\langlep_T\rangle$ dependence of identified light flavour charged hadrons on$\sqrt{(\frac{dN}{dy})/S_{\perp}}$, relevant scale in gluon saturation picture,is studied from $\sqrt{s_{NN}}$=7.7 GeV up to 5.02 TeV. This study is extendedto the slopes of the $\langle p_T\rangle$ dependence on the particle mass andthe $\langle\beta_T\rangle$ parameter from Boltzmann-Gibbs Blast Wave (BGBW)fits of the $p_T$ spectra. A systematic decrease of the slope of the $\langlep_T\rangle$ dependence on $\sqrt{(\frac{dN}{dy})/S_{\perp}}$ from BES to theLHC energies is evidenced. While for the RHIC energies, within the experimentalerrors, the $\langle p_T\rangle$/$\sqrt{(\frac{dN}{dy})/S_{\perp}}$ does notdepend on centrality, at the LHC energies a deviation from a linear behaviouris observed towards the most central collisions. The influence of the coronacontribution to the observed trends is discussed. The slopes of the $\langlep_T\rangle$ particle mass dependence and the $\langle\beta_T\rangle$ parameterfrom BGBW fits scale well with $\sqrt{(\frac{dN}{dy})/S_{\perp}}$. Similarsystematic trends for pp at $\sqrt{s}$=7 TeV are in a good agreement with theones corresponding to Pb-Pb collisions at $\sqrt{s_{NN}}$=2.76 TeV and 5.02 TeVpointing to a system size independent behaviour.

Geometrical scaling for energies available at the BNL Relativistic Heavy Ion Collider to those at the CERN Large Hadron Collider