# Skewness, kurtosis, and the fifth and sixth order cumulants of net baryon-number distributions from lattice QCD confront high-statistics STAR data

## Abstract

We present new results on up to 6th order cumulants of net baryon-number fluctuations at small values of the baryon chemical potential, µB, obtained in lattice QCD calculations with physical values of light and strange quark masses. Representation of the Taylor expansions of higher order cumulants in terms of the ratio of the two lowest order cumulants, M_{B}/σ^{2} B = $χ$ $$^{B}_{1}$$ (T, µ_{B})/$χ$ $$^{B}_{2}$$ (T,µ_{B}), allows for a parameter free comparison with data on net proton-number cumulants obtained by the STAR Collaboration in the Beam Energy Scan at RHIC. We show that recent high statistics data on skewness and kurtosis ratios of net proton-number distributions, obtained at beam energy $$ \sqrt{s_{NN}}$$ = 54.4 GeV, agree well with lattice QCD results on cumulants of net baryon-number fluctuations close to the pseudo-critical temperature, T_{pc}(µ_{B}), for the chiral transition in QCD. We also present first results from a next-to-leading order expansion of 5th and 6th order cumulants on the line of pseudo-critical temperatures.

- Authors:

- Publication Date:

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

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF); National Natural Science Foundation of China (NSFC)

- Contributing Org.:
- HotQCD Collaboration

- OSTI Identifier:
- 1608179

- Alternate Identifier(s):
- OSTI ID: 1614699

- Report Number(s):
- BNL-213820-2020-JAAM

Journal ID: ISSN 2470-0010; PRVDAQ; 074502

- Grant/Contract Number:
- AC05-00OR22725; AC02-05CH11231; AC02-06CH11357; SC0012704; PHY-1812332

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 101 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; lattice QCD; QCD phase transitions; relativistic heavy-ion collisions

### Citation Formats

```
Bazavov, A., Bollweg, D., Ding, H. -T., Enns, P., Goswami, J., Hegde, P., Kaczmarek, O., Karsch, F., Larsen, R., Mukherjee, Swagato, Ohno, H., Petreczky, P., Schmidt, C., Sharma, S., Steinbrecher, P., and HotQCD Collaboration. Skewness, kurtosis, and the fifth and sixth order cumulants of net baryon-number distributions from lattice QCD confront high-statistics STAR data. United States: N. p., 2020.
Web. doi:10.1103/PhysRevD.101.074502.
```

```
Bazavov, A., Bollweg, D., Ding, H. -T., Enns, P., Goswami, J., Hegde, P., Kaczmarek, O., Karsch, F., Larsen, R., Mukherjee, Swagato, Ohno, H., Petreczky, P., Schmidt, C., Sharma, S., Steinbrecher, P., & HotQCD Collaboration. Skewness, kurtosis, and the fifth and sixth order cumulants of net baryon-number distributions from lattice QCD confront high-statistics STAR data. United States. https://doi.org/10.1103/PhysRevD.101.074502
```

```
Bazavov, A., Bollweg, D., Ding, H. -T., Enns, P., Goswami, J., Hegde, P., Kaczmarek, O., Karsch, F., Larsen, R., Mukherjee, Swagato, Ohno, H., Petreczky, P., Schmidt, C., Sharma, S., Steinbrecher, P., and HotQCD Collaboration. Fri .
"Skewness, kurtosis, and the fifth and sixth order cumulants of net baryon-number distributions from lattice QCD confront high-statistics STAR data". United States. https://doi.org/10.1103/PhysRevD.101.074502.
```

```
@article{osti_1608179,
```

title = {Skewness, kurtosis, and the fifth and sixth order cumulants of net baryon-number distributions from lattice QCD confront high-statistics STAR data},

author = {Bazavov, A. and Bollweg, D. and Ding, H. -T. and Enns, P. and Goswami, J. and Hegde, P. and Kaczmarek, O. and Karsch, F. and Larsen, R. and Mukherjee, Swagato and Ohno, H. and Petreczky, P. and Schmidt, C. and Sharma, S. and Steinbrecher, P. and HotQCD Collaboration},

abstractNote = {We present new results on up to 6th order cumulants of net baryon-number fluctuations at small values of the baryon chemical potential, µB, obtained in lattice QCD calculations with physical values of light and strange quark masses. Representation of the Taylor expansions of higher order cumulants in terms of the ratio of the two lowest order cumulants, MB/σ2 B = $χ$ $^{B}_{1}$ (T, µB)/$χ$ $^{B}_{2}$ (T,µB), allows for a parameter free comparison with data on net proton-number cumulants obtained by the STAR Collaboration in the Beam Energy Scan at RHIC. We show that recent high statistics data on skewness and kurtosis ratios of net proton-number distributions, obtained at beam energy $ \sqrt{s_{NN}}$ = 54.4 GeV, agree well with lattice QCD results on cumulants of net baryon-number fluctuations close to the pseudo-critical temperature, Tpc(µB), for the chiral transition in QCD. We also present first results from a next-to-leading order expansion of 5th and 6th order cumulants on the line of pseudo-critical temperatures.},

doi = {10.1103/PhysRevD.101.074502},

journal = {Physical Review D},

number = 7,

volume = 101,

place = {United States},

year = {2020},

month = {4}

}

https://doi.org/10.1103/PhysRevD.101.074502

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