Geometrical Scaling and the Dependence of the Average Transverse Momentum on the Multiplicity and Energy for the ALICE Experiment

We review the recent ALICE data on charged particle multiplicity in p-p collisions, and show that it exhibits Geometrical Scaling (GS) with energy dependence given with characteristic exponent $\lambda=0.22$. Next, starting from the GS hypothesis and using results of the Color Glass Condensate effective theory, we calculate $< p_{\text{T}}>$ as a function $N_{\rm ch}$ including dependence on the scattering energy $W$. We show that $< p_{\text{T}}>$ both in p-p and p-Pb collisions scales in terms of scaling variable $(W/W_{0})^{\lambda/(2+\lambda)}% \sqrt{N_{\mathrm{ch}}/S_{\bot}}$ where $S_{\bot}$ is multiplicity dependent interaction area in the transverse plane. Furthermore, we discuss how the behavior of the interaction radius $R$ at large multiplicities affects the mean $p_{\mathrm{T}}$ dependence on $N_{\rm ch}$, and make a prediction that $< p_{\text{T}}>$ at high multiplicity should reach an energy independent limit.