# 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 (σ$$2\atop{B}$$), skewness (S _{B}) and kurtosis (κ _{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 √sNN ≥ 19.6 GeV. We show that the difference in cumulant ratios for the mean net baryon-number, M _{B}/σ$$2\atop{B}$$ = χ$$B\atop{1}$$ (T, µ _{B})/χ$$B\atop{2}$$ (T, µ _{B}) and the normalized skewness, S _{B}σ _{B} = χ$$B\atop{3}$$ (T, µB)/χ2 (T, µB ), nat-urally arises in QCD thermodynamics. Moreover, we establish a close relation between skewness and kurtosis ratios, S _{B}σ$$B\atop{3}$$/M _{B} = χ$$B\atop{3}$$ (T, µ _{B})/χ$$B\atop{1}$$ (T,µ _{B}) and κ _{B}σ$$2\atop{B}$$ = χ$$B\atop{4}$$ (T,μ _{B})/χ$$B\atop{2}$$ (T,μ _{B}), valid at small values of the baryon chemical potential.

- Authors:

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Brookhaven National Lab. (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; TRN: US1802771]

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

- Resource Type:
- 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. https://www.osti.gov/servlets/purl/1431281.
```

```
@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 (σ$2\atop{B}$), skewness (SB) and kurtosis (κB) 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 √sNN ≥ 19.6 GeV. We show that the difference in cumulant ratios for the mean net baryon-number, MB/σ$2\atop{B}$ = χ$B\atop{1}$ (T, µB)/χ$B\atop{2}$ (T, µB) and the normalized skewness, SBσB = χ$B\atop{3}$ (T, µB)/χ2 (T, µB ), nat-urally arises in QCD thermodynamics. Moreover, we establish a close relation between skewness and kurtosis ratios, SBσ$B\atop{3}$/MB = χ$B\atop{3}$ (T, µB)/χ$B\atop{1}$ (T,µB) and κBσ$2\atop{B}$ = χ$B\atop{4}$ (T,μB)/χ$B\atop{2}$ (T,μB), 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 = {2017},

month = {10}

}

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Works referenced in this record:

##
Freeze-Out Conditions in Heavy Ion Collisions from QCD Thermodynamics

journal, November 2012

- Bazavov, A.; Ding, H. -T.; Hegde, P.
- Physical Review Letters, Vol. 109, Issue 19

##
Acceptance corrections to net baryon and net charge cumulants

journal, October 2012

- Bzdak, Adam; Koch, Volker
- Physical Review C, Vol. 86, Issue 4

##
Universal Off-Equilibrium Scaling of Critical Cumulants in the QCD Phase Diagram

journal, November 2016

- Mukherjee, Swagato; Venugopalan, Raju; Yin, Yi
- Physical Review Letters, Vol. 117, Issue 22

##
Higher Moments of Net Proton Multiplicity Distributions at RHIC

journal, July 2010

- Aggarwal, M. M.; Ahammed, Z.; Alakhverdyants, A. V.
- Physical Review Letters, Vol. 105, Issue 2

##
Phase boundary for the chiral transition in ( $2+1$ )-flavor QCD at small values of the chemical potential

journal, January 2011

- Kaczmarek, O.; Karsch, F.; Laermann, E.
- Physical Review D, Vol. 83, Issue 1

##
Chiral and deconfinement aspects of the QCD transition

journal, March 2012

- Bazavov, A.; Bhattacharya, T.; Cheng, M.
- Physical Review D, Vol. 85, Issue 5

##
Review of Particle Physics

journal, July 2012

- Beringer, J.; Arguin, J. -F.; Barnett, R. M.
- Physical Review D, Vol. 86, Issue 1

##
Slowing out of equilibrium near the QCD critical point

journal, April 2000

- Berdnikov, Boris; Rajagopal, Krishna
- Physical Review D, Vol. 61, Issue 10

##
Effects of kinematic cuts on net electric charge fluctuations

journal, March 2016

- Karsch, Frithjof; Morita, Kenji; Redlich, Krzysztof
- Physical Review C, Vol. 93, Issue 3

##
Proton-Number Fluctuation as a Signal of the QCD Critical End Point

journal, September 2003

- Hatta, Y.; Stephanov, M. A.
- Physical Review Letters, Vol. 91, Issue 10

##
Color superconductivity and chiral symmetry restoration at non-zero baryon density and temperature

journal, January 1999

- Berges, Jürgen; Rajagopal, Krishna
- Nuclear Physics B, Vol. 538, Issue 1-2

##
Measurement of higher cumulants of net-charge multiplicity distributions in $\mathrm{Au}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}\mathrm{Au}$ collisions at $\sqrt{{s}_{NN}}=7.7\u2013200\phantom{\rule{0.28em}{0ex}}\mathrm{GeV}$

journal, January 2016

- Adare, A.; Afanasiev, S.; Aidala, C.
- Physical Review C, Vol. 93, Issue 1

##
Freeze-Out Parameters: Lattice Meets Experiment

journal, August 2013

- Borsányi, S.; Fodor, Z.; Katz, S. D.
- Physical Review Letters, Vol. 111, Issue 6

##
Curvature of the chiral pseudocritical line in QCD: Continuum extrapolated results

journal, September 2015

- Bonati, Claudio; D’Elia, Massimo; Mariti, Marco
- Physical Review D, Vol. 92, Issue 5

##
Higher Moments of Net-Particle Multiplicity Distributions

journal, December 2016

- Thäder, Jochen
- Nuclear Physics A, Vol. 956

##
Non-equilibrium time evolution of higher order cumulants of conserved charges and event-by-event analysis

journal, January 2014

- Kitazawa, Masakiyo; Asakawa, Masayuki; Ono, Hirosato
- Physics Letters B, Vol. 728

##
Local efficiency corrections to higher order cumulants

journal, February 2015

- Bzdak, A.; Koch, V.
- Physical Review C, Vol. 91, Issue 2

##
QCD equation of state to $\mathcal{O}({\mu}_{B}^{6})$ from lattice QCD

journal, March 2017

- Bazavov, A.; Ding, H. -T.; Hegde, P.
- Physical Review D, Vol. 95, Issue 5

##
Baryon-Strangeness Correlations: A Diagnostic of Strongly Interacting Matter

journal, October 2005

- Koch, V.; Majumder, A.; Randrup, J.
- Physical Review Letters, Vol. 95, Issue 18

##
Erratum: Relation between baryon number fluctuations and experimentally observed proton number fluctuations in relativistic heavy ion collisions [Phys. Rev. C **86** , 024904 (2012)]

journal, December 2012

- Kitazawa, Masakiyo; Asakawa, Masayuki
- Physical Review C, Vol. 86, Issue 6

##
Critical line of $2+1$ flavor QCD: Toward the continuum limit

journal, January 2016

- Cea, Paolo; Cosmai, Leonardo; Papa, Alessandro
- Physical Review D, Vol. 93, Issue 1

##
Fluctuations of conserved charges in relativistic heavy ion collisions: An introduction

journal, September 2016

- Asakawa, Masayuki; Kitazawa, Masakiyo
- Progress in Particle and Nuclear Physics, Vol. 90

##
Curvature of the freeze-out line in heavy ion collisions

journal, January 2016

- Bazavov, A.; Ding, H. -T.; Hegde, P.
- Physical Review D, Vol. 93, Issue 1

##
Equation of state in ( $2+1$ )-flavor QCD

journal, November 2014

- Bazavov, A.; Bhattacharya, Tanmoy; DeTar, C.
- Physical Review D, Vol. 90, Issue 9

##
Hadron freeze-out and Unruh radiation

journal, July 2015

- Castorina, Paolo; Iorio, Alfredo; Satz, Helmut
- International Journal of Modern Physics E, Vol. 24, Issue 07

##
Beam Energy Dependence of Moments of the Net-Charge Multiplicity Distributions in $\mathrm{Au}+\mathrm{Au}$ Collisions at RHIC

journal, August 2014

- Adamczyk, L.; Adkins, J. K.; Agakishiev, G.
- Physical Review Letters, Vol. 113, Issue 9

##
The QCD phase diagram from analytic continuation

journal, December 2015

- Bellwied, R.; Borsanyi, S.; Fodor, Z.
- Physics Letters B, Vol. 751

##
Search for the QCD critical point with fluctuations of conserved quantities in relativistic heavy-ion collisions at RHIC: an overview

journal, July 2017

- Luo, Xiaofeng; Xu, Nu
- Nuclear Science and Techniques, Vol. 28, Issue 8

##
Thermodynamics of strong-interaction matter from lattice QCD

journal, October 2015

- Ding, Heng-Tong; Karsch, Frithjof; Mukherjee, Swagato
- International Journal of Modern Physics E, Vol. 24, Issue 10

##
Comparison of chemical freeze-out criteria in heavy-ion collisions

journal, March 2006

- Cleymans, J.; Oeschler, H.; Redlich, K.
- Physical Review C, Vol. 73, Issue 3

##
Acceptance dependence of fluctuation measures near the QCD critical point

journal, March 2016

- Ling, Bo; Stephanov, Mikhail A.
- Physical Review C, Vol. 93, Issue 3

##
Additional Strange Hadrons from QCD Thermodynamics and Strangeness Freezeout in Heavy Ion Collisions

journal, August 2014

- Bazavov, A.; Ding, H. -T.; Hegde, P.
- Physical Review Letters, Vol. 113, Issue 7

##
Real-time evolution of non-Gaussian cumulants in the QCD critical regime

journal, September 2015

- Mukherjee, Swagato; Venugopalan, Raju; Yin, Yi
- Physical Review C, Vol. 92, Issue 3

##
Chiral restoration at finite density and temperature

journal, November 1989

- Masayuki, Asakawa; Koichi, Yazaki
- Nuclear Physics A, Vol. 504, Issue 4

##
Hadronic fluctuations at the QCD phase transition

journal, February 2006

- Ejiri, S.; Karsch, F.; Redlich, K.
- Physics Letters B, Vol. 633, Issue 2-3

##
Phase diagram of QCD

journal, September 1998

- Halasz, M. A.; Jackson, A. D.; Shrock, R. E.
- Physical Review D, Vol. 58, Issue 9

##
Relation between baryon number fluctuations and experimentally observed proton number fluctuations in relativistic heavy ion collisions

journal, August 2012

- Kitazawa, Masakiyo; Asakawa, Masayuki
- Physical Review C, Vol. 86, Issue 2

##
Lattice QCD predictions for shapes of event distributions along the freezeout curve in heavy-ion collisions

journal, February 2011

- Gavai, R. V.; Gupta, Sourendu
- Physics Letters B, Vol. 696, Issue 5

##
Hadron production in central nucleus–nucleus collisions at chemical freeze-out

journal, June 2006

- Andronic, A.; Braun-Munzinger, P.; Stachel, J.
- Nuclear Physics A, Vol. 772, Issue 3-4

##
Hadron yields and the phase diagram of strongly interacting matter

journal, November 2014

- Floris, M.
- Nuclear Physics A, Vol. 931

Works referencing / citing this record:

##
Overlap between Lattice QCD and HRG with in-medium effects and parity doubling

journal, January 2018

- Morita, Kenji; Sasaki, Chihiro; Lo, Pok Man
- EPJ Web of Conferences, Vol. 171