L\'evy walk of pions in heavy-ion collisions

TL;DR

This paper investigates the spatial distribution of pions in heavy-ion collisions, demonstrating through simulations that their freeze-out positions follow a Le9vy-stable distribution, revealing complex underlying dynamics.

Contribution

It introduces a three-dimensional analysis of pion freeze-out distributions and shows these follow Le9vy-stable distributions in high-energy collision simulations.

Findings

Pion freeze-out distributions exhibit heavy tails.

Simulated distributions are well-described by Le9vy-stable models.

The process chain leads to Le9vy-stable step length distributions.

Abstract

The process of L\'evy walk, i.e., movement patterns described by heavy-tailed random walks, plays a role in various phenomena, from chemical and microbiological systems through marine predators to climate change. Recent experiments have suggested that this phenomenon also appears in heavy-ion collisions. However, the theoretical interpretation supporting such findings is still debated. In high-energy collisions of heavy nuclei, the strongly interacting Quark Gluon Plasma is created, which, similarly to the early Universe, undergoes a rapid expansion and transition back to hadronic matter. In the subsequent expanding hadron gas, particles interact until kinetic freeze-out, when their momenta stop changing, and they freely transition toward the detectors. Measuring spatial freeze-out distributions is a crucial tool in understanding the dynamics of the created matter and the interactions among its constituents. In this paper, we introduce a three-dimensional analysis of the spatial freeze-out distribution of pions (the most abundant particles in such collisions). Utilising Monte-Carlo simulations of high-energy collisions, we show that the chain of processes ending in a final state pion has a step length distribution leading to L\'evy-stable distributions. Subsequently, we show that simulated pion freeze-out distributions indeed exhibit heavy tails and can be described by a three-dimensional elliptically contoured symmetric L\'evy-stable distribution.