# Skewness and kurtosis of net baryon-number distributions at small values of the baryon chemical potential

## Abstract

In this paper, we present results for the ratios of mean (M _{B}), variance (Ïƒ$$2\atop{B}$$), skewness (S _{B}) and kurtosis (Îº _{B}) of net baryon-number fluctuations obtained in lattice QCD calculations with physical values of light and strange quark masses. Using next-to-leading order Taylor expansions in baryon chemical potential we find that qualitative features of these ratios closely resemble the corresponding experimentally measured cumulants ratios of net proton-number fluctuations for beam energies down to âˆšsNN â‰¥ 19.6 GeV. We show that the difference in cumulant ratios for the mean net baryon-number, M _{B}/Ïƒ$$2\atop{B}$$ = Ï‡$$B\atop{1}$$ (T, Âµ _{B})/Ï‡$$B\atop{2}$$ (T, Âµ _{B}) and the normalized skewness, S _{B}Ïƒ _{B} = Ï‡$$B\atop{3}$$ (T, ÂµB)/Ï‡2 (T, ÂµB ), nat-urally arises in QCD thermodynamics. Moreover, we establish a close relation between skewness and kurtosis ratios, S _{B}Ïƒ$$B\atop{3}$$/M _{B} = Ï‡$$B\atop{3}$$ (T, Âµ _{B})/Ï‡$$B\atop{1}$$ (T,Âµ _{B}) and Îº _{B}Ïƒ$$2\atop{B}$$ = Ï‡$$B\atop{4}$$ (T,Î¼ _{B})/Ï‡$$B\atop{2}$$ (T,Î¼ _{B}), valid at small values of the baryon chemical potential.

- Authors:

- Publication Date:

- Research Org.:
- Brookhaven National Laboratory (BNL), Upton, NY (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); BNL Program Development

- Contributing Org.:
- HotQCD Collaboration

- OSTI Identifier:
- 1431281

- Alternate Identifier(s):
- OSTI ID: 1405219

- Report Number(s):
- BNL-203396-2018-JAAM

Journal ID: ISSN 2470-0010; PRVDAQ

- Grant/Contract Number:
- SC0012704; AC52-07NA27344; SC001270

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 96; Journal Issue: 7; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Bazavov, A., Ding, H. -T., Hegde, P., Kaczmarek, O., Karsch, F., Laermann, E., Mukherjee, Swagato, Ohno, H., Petreczky, P., Rinaldi, E., Sandmeyer, H., Schmidt, C., Schroeder, Chris, Sharma, S., Soeldner, W., Soltz, R. A., Steinbrecher, P., and Vranas, P. M.
```*Skewness and kurtosis of net baryon-number distributions at small values of the baryon chemical potential*. United States: N. p., 2017.
Web. doi:10.1103/PhysRevD.96.074510.

```
Bazavov, A., Ding, H. -T., Hegde, P., Kaczmarek, O., Karsch, F., Laermann, E., Mukherjee, Swagato, Ohno, H., Petreczky, P., Rinaldi, E., Sandmeyer, H., Schmidt, C., Schroeder, Chris, Sharma, S., Soeldner, W., Soltz, R. A., Steinbrecher, P., & Vranas, P. M.
```*Skewness and kurtosis of net baryon-number distributions at small values of the baryon chemical potential*. United States. doi:10.1103/PhysRevD.96.074510.

```
Bazavov, A., Ding, H. -T., Hegde, P., Kaczmarek, O., Karsch, F., Laermann, E., Mukherjee, Swagato, Ohno, H., Petreczky, P., Rinaldi, E., Sandmeyer, H., Schmidt, C., Schroeder, Chris, Sharma, S., Soeldner, W., Soltz, R. A., Steinbrecher, P., and Vranas, P. M. Fri .
"Skewness and kurtosis of net baryon-number distributions at small values of the baryon chemical potential". United States.
doi:10.1103/PhysRevD.96.074510.
```

```
@article{osti_1431281,
```

title = {Skewness and kurtosis of net baryon-number distributions at small values of the baryon chemical potential},

author = {Bazavov, A. and Ding, H. -T. and Hegde, P. and Kaczmarek, O. and Karsch, F. and Laermann, E. and Mukherjee, Swagato and Ohno, H. and Petreczky, P. and Rinaldi, E. and Sandmeyer, H. and Schmidt, C. and Schroeder, Chris and Sharma, S. and Soeldner, W. and Soltz, R. A. and Steinbrecher, P. and Vranas, P. M.},

abstractNote = {In this paper, we present results for the ratios of mean (MB), variance (Ïƒ$2\atop{B}$), skewness (SB) and kurtosis (ÎºB) of net baryon-number fluctuations obtained in lattice QCD calculations with physical values of light and strange quark masses. Using next-to-leading order Taylor expansions in baryon chemical potential we find that qualitative features of these ratios closely resemble the corresponding experimentally measured cumulants ratios of net proton-number fluctuations for beam energies down to âˆšsNN â‰¥ 19.6 GeV. We show that the difference in cumulant ratios for the mean net baryon-number, MB/Ïƒ$2\atop{B}$ = Ï‡$B\atop{1}$ (T, ÂµB)/Ï‡$B\atop{2}$ (T, ÂµB) and the normalized skewness, SBÏƒB = Ï‡$B\atop{3}$ (T, ÂµB)/Ï‡2 (T, ÂµB ), nat-urally arises in QCD thermodynamics. Moreover, we establish a close relation between skewness and kurtosis ratios, SBÏƒ$B\atop{3}$/MB = Ï‡$B\atop{3}$ (T, ÂµB)/Ï‡$B\atop{1}$ (T,ÂµB) and ÎºBÏƒ$2\atop{B}$ = Ï‡$B\atop{4}$ (T,Î¼B)/Ï‡$B\atop{2}$ (T,Î¼B), valid at small values of the baryon chemical potential.},

doi = {10.1103/PhysRevD.96.074510},

journal = {Physical Review D},

number = 7,

volume = 96,

place = {United States},

year = {Fri Oct 27 00:00:00 EDT 2017},

month = {Fri Oct 27 00:00:00 EDT 2017}

}

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