Chiral crossover in QCD at zero and non-zero chemical potentials

A. Bazavov (Department of Computational Mathematics, Science and Engineering, Department of Physics and Astronomy, Michigan State University, East Lansing, USA) ; H.T. Ding (Key Laboratory of Quark & Lepton Physics (MOE), Institute of Particle Physics, Central China Normal University, Wuhan, China) ; P. Hegde (Center for High Energy Physics, Indian Institute of Science, Bangaluru, India) ; O. Kaczmarek (Key Laboratory of Quark & Lepton Physics (MOE), Institute of Particle Physics, Central China Normal University, Wuhan, China; Fakultät für Physik, Universität Bielefeld, Bielefeld, Germany) ; F. Karsch (Fakultät für Physik, Universität Bielefeld, Bielefeld, Germany; Physics Department, Brookhaven National Laboratory, Upton, USA) ; et al. - Show all 17 authors

We present results for pseudo-critical temperatures of QCD chiral crossovers at zero and non-zero values of baryon (B), strangeness (S), electric charge (Q), and isospin (I) chemical potentials μX=B,Q,S,I. The results were obtained using lattice QCD calculations carried out with two degenerate up and down dynamical quarks and a dynamical strange quark, with quark masses corresponding to physical values of pion and kaon masses in the continuum limit. By parameterizing pseudo-critical temperatures as Tc(μX)=Tc(0)[1−κ2X(μX/Tc(0))2−κ4X(μX/Tc(0))4], we determined κ2X and κ4X from Taylor expansions of chiral observables in μX. We obtained a precise result for Tc(0)=(156.5±1.5) MeV. For analogous thermal conditions at the chemical freeze-out of relativistic heavy-ion collisions, i.e., μS(T,μB) and μQ(T,μB) fixed from strangeness-neutrality and isospin-imbalance, we found κ2B=0.012(4) and κ4B=0.000(4). For μB≲300 MeV, the chemical freeze-out takes place in the vicinity of the QCD phase boundary, which coincides with the lines of constant energy density of 0.42(6)GeV/fm3 and constant entropy density of 3.7(5)fm−3.

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      "value": "We present results for pseudo-critical temperatures of QCD chiral crossovers at zero and non-zero values of baryon (B), strangeness (S), electric charge (Q), and isospin (I) chemical potentials <math><msub><mrow><mi>\u03bc</mi></mrow><mrow><mi>X</mi><mo>=</mo><mi>B</mi><mo>,</mo><mi>Q</mi><mo>,</mo><mi>S</mi><mo>,</mo><mi>I</mi></mrow></msub></math>. The results were obtained using lattice QCD calculations carried out with two degenerate up and down dynamical quarks and a dynamical strange quark, with quark masses corresponding to physical values of pion and kaon masses in the continuum limit. By parameterizing pseudo-critical temperatures as <math><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><msub><mrow><mi>\u03bc</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>)</mo><mo>=</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mn>0</mn><mo>)</mo><mrow><mo>[</mo><mn>1</mn><mo>\u2212</mo><msubsup><mrow><mi>\u03ba</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>X</mi></mrow></msubsup><msup><mrow><mo>(</mo><msub><mrow><mi>\u03bc</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>/</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mn>0</mn><mo>)</mo><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>\u2212</mo><msup><mrow><msub><mrow><mi>\u03ba</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow><mrow><mi>X</mi></mrow></msup><msup><mrow><mo>(</mo><msub><mrow><mi>\u03bc</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>/</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mn>0</mn><mo>)</mo><mo>)</mo></mrow><mrow><mn>4</mn></mrow></msup><mo>]</mo></mrow></math>, we determined <math><msubsup><mrow><mi>\u03ba</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>X</mi></mrow></msubsup></math> and <math><msubsup><mrow><mi>\u03ba</mi></mrow><mrow><mn>4</mn></mrow><mrow><mi>X</mi></mrow></msubsup></math> from Taylor expansions of chiral observables in <math><msub><mrow><mi>\u03bc</mi></mrow><mrow><mi>X</mi></mrow></msub></math>. We obtained a precise result for <math><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mn>0</mn><mo>)</mo><mo>=</mo><mo>(</mo><mn>156.5</mn><mo>\u00b1</mo><mn>1.5</mn><mo>)</mo></math> MeV. For analogous thermal conditions at the chemical freeze-out of relativistic heavy-ion collisions, i.e., <math><msub><mrow><mi>\u03bc</mi></mrow><mrow><mi>S</mi></mrow></msub><mo>(</mo><mi>T</mi><mo>,</mo><msub><mrow><mi>\u03bc</mi></mrow><mrow><mi>B</mi></mrow></msub><mo>)</mo></math> and <math><msub><mrow><mi>\u03bc</mi></mrow><mrow><mi>Q</mi></mrow></msub><mo>(</mo><mi>T</mi><mo>,</mo><msub><mrow><mi>\u03bc</mi></mrow><mrow><mi>B</mi></mrow></msub><mo>)</mo></math> fixed from strangeness-neutrality and isospin-imbalance, we found <math><msup><mrow><msub><mrow><mi>\u03ba</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow><mrow><mi>B</mi></mrow></msup><mo>=</mo><mn>0.012</mn><mo>(</mo><mn>4</mn><mo>)</mo></math> and <math><msubsup><mrow><mi>\u03ba</mi></mrow><mrow><mn>4</mn></mrow><mrow><mi>B</mi></mrow></msubsup><mo>=</mo><mn>0.000</mn><mo>(</mo><mn>4</mn><mo>)</mo></math>. For <math><msub><mrow><mi>\u03bc</mi></mrow><mrow><mi>B</mi></mrow></msub><mo>\u2272</mo><mn>300</mn></math> MeV, the chemical freeze-out takes place in the vicinity of the QCD phase boundary, which coincides with the lines of constant energy density of <math><mn>0.42</mn><mo>(</mo><mn>6</mn><mo>)</mo><mspace width=\"0.25em\"></mspace><msup><mrow><mtext>GeV/fm</mtext></mrow><mrow><mn>3</mn></mrow></msup></math> and constant entropy density of <math><mn>3.7</mn><mo>(</mo><mn>5</mn><mo>)</mo><mspace width=\"0.25em\"></mspace><msup><mrow><mtext>fm</mtext></mrow><mrow><mo>\u2212</mo><mn>3</mn></mrow></msup></math>."
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Published on:
31 July 2019
Publisher:
Elsevier
Published in:
Physics Letters B , Volume 795 C (2019)

Pages 15-21
DOI:
https://doi.org/10.1016/j.physletb.2019.05.013
Copyrights:
The Author(s)
Licence:
CC-BY-3.0
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