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

TL;DR

This paper analyzes ALICE data showing geometrical scaling in charged particle multiplicity and predicts how average transverse momentum depends on multiplicity and energy, using the Color Glass Condensate theory.

Contribution

It introduces a model linking average transverse momentum to multiplicity and energy based on geometrical scaling and the Color Glass Condensate framework.

Findings

Charged particle multiplicity exhibits geometrical scaling with energy.

Average transverse momentum scales with multiplicity and energy via a specific variable.

At high multiplicities, the average transverse momentum approaches an energy-independent limit.

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 $N_{\rm ch}$ 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.