Chiral transition in a finite system and possible use of finite size scaling in relativistic heavy ion collisions

TL;DR

This paper studies how finite system sizes affect the chiral phase transition in strong interactions, suggesting finite-size scaling as a useful tool for analyzing experimental data from heavy ion collisions.

Contribution

It introduces a finite-size scaling approach to analyze the chiral transition in relativistic heavy ion collisions, highlighting its potential in identifying the critical endpoint.

Findings

Finite-size effects significantly modify the chiral transition line.

Finite-size scaling can aid in detecting the critical endpoint.

Corrections are important for interpreting experimental signatures.

Abstract

We investigate finite-size effects on the chiral phase diagram of strong interactions within the linear sigma model coupled to quarks. We estimate the modification of the pseudocritical transition line and isentropic trajectories for sizes that are representative of the systems created in relativistic heavy ion collision experiments. The corrections are clearly non-negligible and might significantly affect signatures of the chiral critical endpoint based on estimates for an infinite system. We argue that a finite-size scaling analysis should be tested in the process of data analysis of the Beam Energy Scan program at RHIC and in future experiments at FAIR-GSI, through the use of full scaling plots and a chi-squared method as tools for searching the critical endpoint.