# Effect of finite particle number sampling on baryon number fluctuations

## TL;DR

This paper investigates how finite particle sampling affects baryon number fluctuation measurements in fluid dynamics simulations, revealing that test-particle sampling reduces overestimation of cumulants and providing analytic formulas for correction.

## Contribution

It introduces a method to suppress sampling artifacts in baryon number cumulant calculations and derives exact formulas for their correction in simplified cases.

## Key findings

- Test-particle sampling reduces overestimation of cumulants.
- Derived analytic formulas accurately describe sampling effects.
- Numerical simulations demonstrate the effectiveness of the correction method.

## Abstract

The effects of finite particle number sampling on the net baryon number cumulants, extracted from fluid dynamical simulations, are studied. The commonly used finite particle number sampling procedure introduces an additional Poissonian (or multinomial if global baryon number conservation is enforced) contribution which increases the extracted moments of the baryon number distribution. If this procedure is applied to a fluctuating fluid dynamics framework one severely overestimates the actual cumulants. We show that the sampling of so called test-particles suppresses the additional contribution to the moments by at least one power of the number of test-particles. We demonstrate this method in a numerical fluid dynamics simulation that includes the effects of spinodal decomposition due to a first order phase transition. Furthermore, in the limit where anti-baryons can be ignored, we derive analytic formulas which capture exactly the effect of particle sampling on the baryon number cumulants. These formulas may be used to test the various numerical particle sampling algorithms.