Based on the recent RHIC and LHC experimental results, the $langle p_Trangle$ 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 extended to the slopes of the $langle p_Trangle$ dependence on the particle mass and the $langlebeta_Trangle$ parameter from Boltzmann-Gibbs Blast Wave (BGBW) fits of the $p_T$ spectra. A systematic decrease of the slope of the $langle p_Trangle$ dependence on $sqrt{(frac{dN}{dy})/S_{perp}}$ from BES to the LHC energies is evidenced. While for the RHIC energies, within the experimental errors, the $langle p_Trangle$/$sqrt{(frac{dN}{dy})/S_{perp}}$ does not depend on centrality, at the LHC energies a deviation from a linear behaviour is observed towards the most central collisions. The influence of the corona contribution to the observed trends is discussed. The slopes of the $langle p_Trangle$ particle mass dependence and the $langlebeta_Trangle$ parameter from BGBW fits scale well with $sqrt{(frac{dN}{dy})/S_{perp}}$. Similar systematic trends for pp at $sqrt{s}$=7 TeV are in a good agreement with the ones corresponding to Pb-Pb collisions at $sqrt{s_{NN}}$=2.76 TeV and 5.02 TeV pointing to a system size independent behaviour.
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