High Multiplicity pp and pA Collisions: Hydrodynamics at its Edge

TL;DR

This paper explores the applicability of hydrodynamics to high-multiplicity pp and pA collisions, analyzing flow behaviors and viscous corrections through analytical models and idealized cases.

Contribution

It provides an analytical study of hydrodynamic behavior and viscous corrections in high-multiplicity small-system collisions, extending understanding beyond numerical simulations.

Findings

Radial flow increases from AA to pA collisions.

Elliptic flow decreases from AA to pA collisions.

Viscous corrections grow from AA to pp but stay manageable.

Abstract

With growing multiplicity, the pp and pA collisions enter the domain where the macroscopic description (thermodynamics and hydrodynamics) becomes applicable. We discuss this situation, first with simplified thought experiments, then with some idealized representative cases, and finally address the real data. For clarity, we don't do it numerically but analytically, using the Gubser solution. We found that the radial flow is expected to increase from central AA to central pA, while the elliptic flow decreases, with higher harmonics being comparable. In the second part of the paper we approach the problem from the opposite side, using a string-based Pomeron model. We extensively study the magnitude and distribution of the viscous corrections, in Navier-Stokes and Israel-Stuart approximations, ending with higher gradient re-summation proposed by Lublinsky and Shuryak. We found those corrections growing, from AA to pA to pp, but remaining at the manageable size even in the last case.