Why mean $p_{\rm T}$ is interesting

TL;DR

This paper explores how the average transverse momentum in high-energy collisions depends on energy and multiplicity, using a saturation model based on the Color Glass Condensate framework, and demonstrates a universal scaling behavior in experimental data.

Contribution

It introduces a scaling variable for mean $p_{\rm T}$ as a function of multiplicity and energy, based on a saturation model of the interaction radius, and confirms this scaling with ALICE data.

Findings

ALICE data exhibits the predicted scaling behavior.

The effective interaction radius scales as the cube root of multiplicity.

A universal behavior of mean $p_{\rm T}$ for high multiplicities is suggested.

Abstract

We discuss energy dependence of mean $p_{\rm T}$ correlation with $N_{\rm ch}$ basing on general features of high energy collisions such as saturation and geometrical scaling. We use Color Glass Condensate calculation of an effective interaction radius that scales as a third root of multiplicity, and then saturates. With this model input we construct scaling variable for $< p_{\rm T} > (N_{\rm ch})$ at different energies both for pp and pPb collisions, and show that recent ALICE data indeed does exhibit this scaling property. We discuss energy dependence of the interaction radius and argue that since the radius cannot grow too large, a universal behavior of $< p_{\rm T} >$ for large multiplicities is expected.