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

Abstract

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 $N_{\mathrm{ch}}$ 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 $(W/W_0{)}^{\lambda /(2+\lambda )}$ where $S_{\perp }$ 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 $N_{\mathrm{ch}}$, and make a prediction that $<p_{\text{T}}>$ at high multiplicity should reach an energy independent limit.

Comments: 15 pages, 7 figures, in v2 one figure and one reference added, v3: version accepted in Phys. Lett. B., some modifications, references added