Different Realizations of Cooper-Frye Sampling with Conservation Laws

TL;DR

This paper compares four sampling algorithms for particle production in heavy ion collision simulations, focusing on how they incorporate conservation laws and affect particle number fluctuations.

Contribution

It introduces and evaluates four different Cooper-Frye sampling algorithms, highlighting the impact of conservation laws on fluctuations and recommending best practices for fluctuation studies.

Findings

Fluctuations are significantly affected by conservation laws in small volumes.

The SPREW and SER algorithms produce fluctuations consistent with canonical ensemble expectations.

The mode sampling algorithm yields overly large fluctuations, unsuitable for fluctuation analysis.

Abstract

Approaches based on viscous hydrodynamics for the hot and dense stage and hadronic transport for the final dilute rescattering stage are successfully applied to the dynamic description of heavy ion reactions at high beam energies. One crucial step in such hybrid approaches is the so called particlization, the transition between the hydrodynamic description to microscopic degrees of freedom. For this purpose, individual particles are sampled on the Cooper-Frye hypersurface. In this work, 4 different realizations of sampling algorithms are compared, where three of them incorporate global conservation laws of quantum numbers in each event. The algorithms are compared within two types of scenarios: simple "box" hypersurface consisting of only one static cell and a typical particlization hypersurface for Au+Au collisions at $\sqrt{s_\mathrm{NN}} = 200$ GeV. For all algorithms the mean multiplicities (or particle spectra) remain unaffected by global conservation laws in the case of large volumes. In contrast, the fluctuations of the particle numbers are affected considerably. The fluctuations of the newly developed SPREW algorithm based on exponential weights and the recently suggested SER algorithm based on ensemble rejection are smaller than without conservation laws and agree with the expectation from the canonical ensemble. The previously applied mode sampling algorithm produces dramatically larger fluctuations, than it is expected in the corresponding microcanonical ensemble, and therefore should be avoided in fluctuation studies. This study might be of interest for investigations of particle fluctuations and correlations, e.g. the suggested signatures for a phase transition or a critical endpoint, in hybrid approaches that are affected by global conservation laws.