Monte Carlo approach to the excluded-volume hadron resonance gas in grand canonical and canonical ensembles

TL;DR

This paper introduces a Monte Carlo method for sampling hadron yields in the hadron resonance gas model, accounting for excluded-volume effects and exact charge conservation, enabling detailed fluctuation analysis.

Contribution

It presents the first Monte Carlo approach for the excluded-volume HRG in the canonical ensemble, incorporating both effects simultaneously.

Findings

MC results match known analytic solutions in the thermodynamic limit

The method accurately captures particle number fluctuations

Finite size effects are effectively estimated

Abstract

The Monte Carlo (MC) procedure for sampling the hadron yields within hadron resonance gas (HRG) model is presented. The effects of excluded-volume due to the finite hadron eigenvolumes and of exact charge conservation within the canonical ensemble (CE) formulation are simultaneously taken into account with the help of the importance sampling technique combined with the rejection sampling. The MC procedure allows one to calculate arbitrary moments of the event-by-event hadron yields. Note that the CE formulation for the excluded-volume HRG has not been considered before. The MC simulations coincide with the known analytic results in the thermodynamic limit for the excluded-volume HRG in the grand canonical ensemble and for the CE of non-interacting particles. The MC procedure is applied to study the simultaneous excluded-volume and CE effects. These effects are considered within the full HRG to calculate the particle number fluctuations and to estimate the finite size effects.