# Effect of finite particle number sampling on baryon number fluctuations

## 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 antibaryons 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.

- Authors:

- Frankfurt Institute for Advanced Studies, Frankfurt am Main (Germany)
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

- OSTI Identifier:
- 1408476

- Alternate Identifier(s):
- OSTI ID: 1395406

- Grant/Contract Number:
- AC02-05CH11231

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review C

- Additional Journal Information:
- Journal Volume: 96; Journal Issue: 3; Journal ID: ISSN 2469-9985

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Steinheimer, Jan, and Koch, Volker.
```*Effect of finite particle number sampling on baryon number fluctuations*. United States: N. p., 2017.
Web. doi:10.1103/PhysRevC.96.034907.

```
Steinheimer, Jan, & Koch, Volker.
```*Effect of finite particle number sampling on baryon number fluctuations*. United States. doi:10.1103/PhysRevC.96.034907.

```
Steinheimer, Jan, and Koch, Volker. Thu .
"Effect of finite particle number sampling on baryon number fluctuations". United States.
doi:10.1103/PhysRevC.96.034907. https://www.osti.gov/servlets/purl/1408476.
```

```
@article{osti_1408476,
```

title = {Effect of finite particle number sampling on baryon number fluctuations},

author = {Steinheimer, Jan and Koch, Volker},

abstractNote = {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 antibaryons 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.},

doi = {10.1103/PhysRevC.96.034907},

journal = {Physical Review C},

number = 3,

volume = 96,

place = {United States},

year = {Thu Sep 28 00:00:00 EDT 2017},

month = {Thu Sep 28 00:00:00 EDT 2017}

}

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