  Based on the recent RHIC and LHC experimental results, the $\langle
p_T\rangle$ 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 extended
to the slopes of the $\langle p_T\rangle$ dependence on the particle mass and
the $\langle\beta_T\rangle$ parameter from Boltzmann-Gibbs Blast Wave (BGBW)
fits of the $p_T$ spectra. A systematic decrease of the slope of the $\langle
p_T\rangle$ 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 $\langle p_T\rangle$/$\sqrt{(\frac{dN}{dy})/S_{\perp}}$ 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 $\langle
p_T\rangle$ particle mass dependence and the $\langle\beta_T\rangle$ 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.
