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

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.