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

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

Phys. Rev. D 96, 074510 – Published 27 October 2017

Abstract

We present results for the ratios of mean ( $M_{B}$ ), variance ( $σ_{B}^{2}$ ), 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 cumulant ratios of net proton-number fluctuations for beam energies down to $\sqrt{s_{N N}} \geq 19.6 GeV$ . We show that the difference in cumulant ratios for the mean net baryon-number, $M_{B} / σ_{B}^{2} = χ_{1}^{B} (T, μ_{B}) / χ_{2}^{B} (T, μ_{B})$ , and the normalized skewness, $S_{B} σ_{B} = χ_{3}^{B} (T, μ_{B}) / χ_{2}^{B} (T, μ_{B})$ , naturally arises in QCD thermodynamics. Moreover, we establish a close relation between skewness and kurtosis ratios, $S_{B} σ_{B}^{3} / M_{B} = χ_{3}^{B} (T, μ_{B}) / χ_{1}^{B} (T, μ_{B})$ and $κ_{B} σ_{B}^{2} = χ_{4}^{B} (T, μ_{B}) / χ_{2}^{B} (T, μ_{B})$ , valid at small values of the baryon chemical potential.

Received 20 August 2017

DOI:https://doi.org/10.1103/PhysRevD.96.074510

Physics Subject Headings (PhySH)

Gauge theories Lattice field theory Quantum chromodynamics Quark-gluon plasma Strong interaction

Particles & Fields

Authors & Affiliations

A. Bazavov¹, H.-T. Ding², P. Hegde³, O. Kaczmarek⁴, F. Karsch^4,5, E. Laermann⁴, Swagato Mukherjee⁵, H. Ohno^5,6, P. Petreczky⁵, E. Rinaldi⁷, H. Sandmeyer⁴, C. Schmidt⁴, Chris Schroeder⁸, S. Sharma⁵, W. Soeldner⁹, R. A. Soltz⁸, P. Steinbrecher^4,5, and P. M. Vranas⁸ (HotQCD Collaboration)

¹Department of Computational Mathematics, Science and Engineering and Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
²Key Laboratory of Quark & Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China
³Center for High Energy Physics, Indian Institute of Science, Bangalore 560012, India
⁴Fakultät für Physik, Universität Bielefeld, D-33615 Bielefeld, Germany
⁵Physics Department, Brookhaven National Laboratory, Upton, New York 11973, USA
⁶Center for Computational Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japan
⁷RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973, USA
⁸Physics Division, Lawrence Livermore National Laboratory, Livermore, California 94550, USA
⁹Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany

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Issue

Vol. 96, Iss. 7 — 1 October 2017

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Physical Review D

covering particles, fields, gravitation, and cosmology