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Title: Chiral matrix model of the semi-QGP in QCD

Abstract

Previously, a matrix model of the region near the transition temperature, in the “semi”quark gluon plasma, was developed for the theory of SU(3) gluons without quarks. In this paper we develop a chiral matrix model applicable to QCD by including dynamical quarks with 2+1 flavors. This requires adding a nonet of scalar fields, with both parities, and coupling these to quarks through a Yukawa coupling, y. Treating the scalar fields in mean field approximation, the effective Lagrangian is computed by integrating out quarks to one loop order. As is standard, the potential for the scalar fields is chosen to be symmetric under the flavor symmetry of SU (3)L × SU(3)R × Z (3) A , except for a term linear in the current quark mass, mqk . In addition, at a nonzero temperature T it is necessary to add a new term, ~ mqk T2 . The parameters of the gluon part of the matrix model are identical to those for the pure glue theory without quarks. The parameters in the chiral matrix model are fixed by the values, at zero temperature, of the pion decay constant and the masses of the pions, kaons, η , and η' . Themore » temperature for the chiral crossover at T$χ$ = 155 MeV is determined by adjusting the Yukawa coupling y . We find reasonable agreement with the results of numerical simulations on the lattice for the pressure and related quantities. In the chiral limit, besides the divergence in the chiral susceptibility there is also a milder divergence in the susceptibility between the Polyakov loop and the chiral order parameter, with critical exponent β $-$ 1 . We compute derivatives with respect to a quark chemical potential to determine the susceptibilities for baryon number, the $χ$2n . Especially sensitive tests are provided by $χ$4 $-$ $χ$2 and by $χ$6 , which changes in sign about T$χ$ . In conclusion, the behavior of the susceptibilities in the chiral matrix model strongly suggests that as the temperature increases from T$χ$ , that the transition to deconfinement is significantly quicker than indicated by the measurements of the (renormalized) Polyakov loop on the lattice.« less

Authors:
 [1];  [2]
  1. Brookhaven National Lab. (BNL), Upton, NY (United States). Dept. of Physics
  2. Brookhaven National Lab. (BNL), Upton, NY (United States). RIKEN Research Center
Publication Date:
Research Org.:
Brookhaven National Lab. (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Under Secretary for Science (S-4)
OSTI Identifier:
1338599
Alternate Identifier(s):
OSTI ID: 1286304
Report Number(s):
BNL-113249-2016-JA
Journal ID: ISSN 2470-0010; PRVDAQ; R&D Project: KB0301020; KB0301020; TRN: US1701735
Grant/Contract Number:  
SC0012704
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 94; Journal Issue: 3; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Semi-Quark Gluon Plasma; QCD

Citation Formats

Pisarski, Robert D., and Skokov, Vladimir V. Chiral matrix model of the semi-QGP in QCD. United States: N. p., 2016. Web. doi:10.1103/PhysRevD.94.034015.
Pisarski, Robert D., & Skokov, Vladimir V. Chiral matrix model of the semi-QGP in QCD. United States. doi:10.1103/PhysRevD.94.034015.
Pisarski, Robert D., and Skokov, Vladimir V. Mon . "Chiral matrix model of the semi-QGP in QCD". United States. doi:10.1103/PhysRevD.94.034015. https://www.osti.gov/servlets/purl/1338599.
@article{osti_1338599,
title = {Chiral matrix model of the semi-QGP in QCD},
author = {Pisarski, Robert D. and Skokov, Vladimir V.},
abstractNote = {Previously, a matrix model of the region near the transition temperature, in the “semi”quark gluon plasma, was developed for the theory of SU(3) gluons without quarks. In this paper we develop a chiral matrix model applicable to QCD by including dynamical quarks with 2+1 flavors. This requires adding a nonet of scalar fields, with both parities, and coupling these to quarks through a Yukawa coupling, y. Treating the scalar fields in mean field approximation, the effective Lagrangian is computed by integrating out quarks to one loop order. As is standard, the potential for the scalar fields is chosen to be symmetric under the flavor symmetry of SU (3)L × SU(3)R × Z (3) A , except for a term linear in the current quark mass, mqk . In addition, at a nonzero temperature T it is necessary to add a new term, ~ mqk T2 . The parameters of the gluon part of the matrix model are identical to those for the pure glue theory without quarks. The parameters in the chiral matrix model are fixed by the values, at zero temperature, of the pion decay constant and the masses of the pions, kaons, η , and η' . The temperature for the chiral crossover at T$χ$ = 155 MeV is determined by adjusting the Yukawa coupling y . We find reasonable agreement with the results of numerical simulations on the lattice for the pressure and related quantities. In the chiral limit, besides the divergence in the chiral susceptibility there is also a milder divergence in the susceptibility between the Polyakov loop and the chiral order parameter, with critical exponent β $-$ 1 . We compute derivatives with respect to a quark chemical potential to determine the susceptibilities for baryon number, the $χ$2n . Especially sensitive tests are provided by $χ$4 $-$ $χ$2 and by $χ$6 , which changes in sign about T$χ$ . In conclusion, the behavior of the susceptibilities in the chiral matrix model strongly suggests that as the temperature increases from T$χ$ , that the transition to deconfinement is significantly quicker than indicated by the measurements of the (renormalized) Polyakov loop on the lattice.},
doi = {10.1103/PhysRevD.94.034015},
journal = {Physical Review D},
number = 3,
volume = 94,
place = {United States},
year = {2016},
month = {8}
}

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Works referenced in this record:

On the nature of the phase transition in SU(N), Sp(2) and E(7) Yang–Mills theory
journal, November 2010


Chiral effective model with the Polyakov loop
journal, July 2004


Effective potential at finite temperature in the standard model
journal, April 1992


Greybody factors and charges in Kerr/CFT
journal, September 2009


Power corrections in the quark-antiquark potential at finite temperature
journal, May 2007


Multiquark hadrons. I. Phenomenology of Q 2 Q ¯ 2 mesons
journal, January 1977


Chiral symmetry breaking and confinement effects on dilepton and photon production around T c
journal, September 2015


Fluctuations of conserved charges at finite temperature from lattice QCD
journal, January 2012

  • Borsányi, Szabolcs; Fodor, Zoltán; Katz, Sándor D.
  • Journal of High Energy Physics, Vol. 2012, Issue 1
  • DOI: 10.1007/JHEP01(2012)138

How instantons solve the U(1) problem
journal, September 1986


Vector meson spectral function and dilepton production rate in a hot and dense medium within an effective QCD approach
journal, February 2015

  • Islam, Chowdhury Aminul; Majumder, Sarbani; Haque, Najmul
  • Journal of High Energy Physics, Vol. 2015, Issue 2
  • DOI: 10.1007/JHEP02(2015)011

Complete high temperature expansions for one-loop finite temperature effects
journal, February 2002


Gross-Witten-Wadia transition in a matrix model of deconfinement
journal, October 2012


β -functions for a S U ( 2 ) matrix model in 2 + ϵ dimensions
journal, August 2006


Mechanism for a next-to-lowest lying scalar meson nonet
journal, February 2000


Introductory lectures on lattice QCD at nonzero baryon number
journal, April 2016


Equation of state in ( 2 + 1 )-flavor QCD
journal, November 2014


Casimir scaling and renormalization of Polyakov loops in large-N gauge theories
journal, May 2012

  • Mykkänen, Anne; Panero, Marco; Rummukainen, Kari
  • Journal of High Energy Physics, Vol. 2012, Issue 5
  • DOI: 10.1007/JHEP05(2012)069

Quark susceptibility in a generalized dynamical quasiparticle model
journal, April 2016


Relevance of matter and glue dynamics for baryon number fluctuations
journal, December 2015


Critical endpoint for deconfinement in matrix and other effective models
journal, June 2012


Vacuum fluctuations and the thermodynamics of chiral models
journal, August 2010


QCD equation of state with almost physical quark masses
journal, January 2008


Thermodynamics of QCD at vanishing density
journal, April 2014


Polyakov loop in 2 + 1 flavor QCD
journal, May 2013


Chiral-Symmetry Breakdown in Large- N Chromodynamics
journal, July 1980


Renormalization group optimized perturbation theory at finite temperatures
journal, December 2015


Roberge-Weiss transition and ’t Hooft loops
journal, May 2013


Meson vacuum phenomenology in a three-flavor linear sigma model with (axial-)vector mesons
journal, January 2013


Fluctuations and correlations in high temperature QCD
journal, December 2015


Susceptibilities and the phase structure of a chiral model with Polyakov loops
journal, April 2007


Full result for the QCD equation of state with <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math> flavors
journal, March 2014


Quark-gluon plasma as a condensate of Z ( 3 ) Wilson lines
journal, November 2000


Freeze-Out Conditions in Heavy Ion Collisions from QCD Thermodynamics
journal, November 2012


Thermodynamics of SU(N) Yang-Mills theories in 2 + 1 dimensions I — The confining phase
journal, June 2011

  • Caselle, Michele; Castagnini, Luca; Feo, Alessandra
  • Journal of High Energy Physics, Vol. 2011, Issue 6
  • DOI: 10.1007/JHEP06(2011)142

Gluon spectral functions and transport coefficients in Yang-Mills theory
journal, November 2014


Thermodynamics of the QCD Plasma and the Large- N Limit
journal, December 2009


Determination of U ( 1 ) A restoration from pion and a 0 -meson screening masses: Toward the chiral regime
journal, January 2016


Phase structure and thermodynamics of QCD
journal, July 2013

  • Herbst, Tina Katharina; Pawlowski, Jan M.; Schaefer, Bernd-Jochen
  • Physical Review D, Vol. 88, Issue 1
  • DOI: 10.1103/PhysRevD.88.014007

Zero point energy of renormalized Wilson loops
journal, October 2009


Constrained effective potential in hot QCD
journal, June 1994


Phase diagram and nucleation in the Polyakov-loop-extended quark-meson truncation of QCD with the unquenched Polyakov-loop potential
journal, May 2016


Chiral symmetry restoration at nonzero temperature in the SU ( 3 ) r × SU ( 3 ) l linear sigma model
journal, September 2000

  • Lenaghan, Jonathan T.; Rischke, Dirk H.; Schaffner-Bielich, Jürgen
  • Physical Review D, Vol. 62, Issue 8
  • DOI: 10.1103/PhysRevD.62.085008

Diquarks and Exotic Spectroscopy
journal, December 2003


Freeze-Out Parameters from Electric Charge and Baryon Number Fluctuations: Is There Consistency?
journal, July 2014


Phenomenological equations of state for the quark-gluon plasma
journal, January 2002


The QCD phase diagram at nonzero quark density
journal, April 2011

  • Endrődi, G.; Fodor, Z.; Katz, S. D.
  • Journal of High Energy Physics, Vol. 2011, Issue 4
  • DOI: 10.1007/JHEP04(2011)001

Interweaving chiral spirals
journal, February 2012


Scale-Invariant Resummed Perturbation at Finite Temperatures
journal, January 2016


Remarks on the chiral phase transition in chromodynamics
journal, January 1984


Gluon Thermodynamics at Intermediate Coupling
journal, March 2010


NNLO hard-thermal-loop thermodynamics for QCD
journal, February 2011


The phase diagram of dense QCD
journal, December 2010


QCD critical region and higher moments for three-flavor models
journal, February 2012


Three-loop HTL gluon thermodynamics at intermediate coupling
journal, August 2010

  • Andersen, Jens O.; Strickland, Michael; Su, Nan
  • Journal of High Energy Physics, Vol. 2010, Issue 8
  • DOI: 10.1007/JHEP08(2010)113

The K / π ratio from condensed Polyakov loops
journal, September 2002


Production and Elliptic Flow of Dileptons and Photons in a Matrix Model of the Quark-Gluon Plasma
journal, February 2015


Chiral symmetry restoration in linear sigma models with different numbers of quark flavors
journal, July 2003


Potential for the phase of the Wilson line at nonzero quark density
journal, February 2000

  • Korthals Altes, C. P.; Pisarski, Robert D.; Sinkovics, Annamaria
  • Physical Review D, Vol. 61, Issue 5
  • DOI: 10.1103/PhysRevD.61.056007

Confinement from correlation functions
journal, August 2013


Non-perturbative dynamics and charge fluctuations in effective chiral models
journal, February 2012


Two-point functions for SU ( 3 ) Polyakov loops near T c
journal, November 2002


Existence of the critical endpoint in the vector meson extended linear sigma model
journal, June 2016


Polyakov SU(3) extended linear- σ model: Sixteen mesonic states in chiral phase structure
journal, January 2015


Glueball in a chiral linear sigma model with vector mesons
journal, September 2011


Review of Particle Physics
journal, August 2014


Lattice QCD at the physical point: Light quark masses
journal, July 2011


Equation of state of hot and dense QCD: resummed perturbation theory confronts lattice data
journal, December 2013

  • Mogliacci, Sylvain; Andersen, Jens O.; Strickland, Michael
  • Journal of High Energy Physics, Vol. 2013, Issue 12
  • DOI: 10.1007/JHEP12(2013)055

Continuum thermodynamics of the SU ( N c ) gluon plasma
journal, December 2010


Interface tension in an SU( N ) gauge theory at high temperature
journal, February 1991

  • Bhattacharya, Tanmoy; Gocksch, Andreas; Altes, Chris Korthals
  • Physical Review Letters, Vol. 66, Issue 8
  • DOI: 10.1103/PhysRevLett.66.998

Equation of state and QCD transition at finite temperature
journal, July 2009


Freeze-Out Parameters: Lattice Meets Experiment
journal, August 2013


Dynamical symmetry breaking in asymptotically free field theories
journal, November 1974


Effective theory of Wilson lines and deconfinement
journal, December 2006


Two-loop perturbative corrections to the thermal effective potential in gluodynamics
journal, January 2014


The phase structure of the Polyakov–quark–meson model beyond mean field
journal, January 2011


Collisional energy loss above the critical temperature in QCD
journal, March 2014


QCD chiral transition, U ( 1 ) A symmetry and the dirac spectrum using domain wall fermions
journal, March 2014


Hadron production in ultra-relativistic nuclear collisions: Quarkyonic matter and a triple point in the phase diagram of QCD
journal, June 2010


Gauge theories with imaginary chemical potential and the phases of QCD
journal, December 1986


The QCD equation of state with dynamical quarks
journal, November 2010

  • Borsányi, Szabolcs; Endrődi, Gergely; Fodor, Zoltán
  • Journal of High Energy Physics, Vol. 2010, Issue 11
  • DOI: 10.1007/JHEP11(2010)077

Fixed scale approach to equation of state in lattice QCD
journal, March 2009


Phases of dense quarks at large
journal, November 2007


Hard thermal loops, to quadratic order, in the background of a spatial ’t Hooft loop
journal, August 2009


Renormalized Polyakov loops in many representations
journal, February 2008


Two-loop hard thermal loop pressure at finite temperature and chemical potential
journal, May 2013


Chiral condensate from renormalization group optimized perturbation
journal, October 2015


Zero interface tensions at the deconfining phase transition for a matrix model of a S U ( ) gauge theory
journal, May 2013


Dense quarks, and the fermion sign problem, in a S U ( N ) matrix model
journal, September 2005


Effective potential for SU(2) Polyakov loops and Wilson loop eigenvalues
journal, September 2013


Effective gluon potential and hybrid approach to Yang-Mills thermodynamics
journal, July 2012


New Look at Scalar Mesons
journal, November 2004


LIGHT SCALARS AS TETRAQUARKS OR TWO-MESON STATES FROM LARGE-N c AND UNITARIZED CHIRAL PERTURBATION THEORY
journal, December 2004


Deconfinement in matrix models about the Gross-Witten point
journal, April 2005


Meson fluctuations and thermodynamics of the Polyakov-loop-extended quark-meson model
journal, July 2010


Correlating the skewness and kurtosis of baryon number distributions
journal, May 2016


High-precision thermodynamics and Hagedorn density of states
journal, September 2009


Chiral and deconfinement aspects of the QCD transition
journal, March 2012


Chiral symmetry restoration at finite temperature in the SU(3) × SU(3) sigma model
journal, November 1983


How π 0 γ γ changes with temperature
journal, December 1997

  • Pisarski, Robert D.; Trueman, T. L.; Tytgat, Michel H. G.
  • Physical Review D, Vol. 56, Issue 11
  • DOI: 10.1103/PhysRevD.56.7077

Small shear viscosity in the semiquark gluon plasma
journal, April 2010


Effective matrix model for deconfinement in pure gauge theories
journal, November 2012


Scalar mesons above and below 1 GeV
journal, August 2002

  • Close, Frank E.; T. rnqvist, Nils A.
  • Journal of Physics G: Nuclear and Particle Physics, Vol. 28, Issue 10
  • DOI: 10.1088/0954-3899/28/10/201

Higher-order ratios of baryon number cumulants
journal, January 2012


Three-loop HTL QCD thermodynamics
journal, August 2011

  • Andersen, Jens O.; Leganger, Lars E.; Strickland, Michael
  • Journal of High Energy Physics, Vol. 2011, Issue 8
  • DOI: 10.1007/JHEP08(2011)053

Role of mesonic fluctuations in the Polyakov loop extended quark-meson model at imaginary chemical potential
journal, October 2011


The phase diagram of nuclear and quark matter at high baryon density
journal, September 2013


QCD and instantons at finite temperature
journal, January 1981

  • Gross, David J.; Pisarski, Robert D.; Yaffe, Laurence G.
  • Reviews of Modern Physics, Vol. 53, Issue 1
  • DOI: 10.1103/RevModPhys.53.43

Quarkyonic chiral spirals
journal, October 2010


Dilepton and photon production in the presence of a nontrivial Polyakov loop
journal, October 2015

  • Hidaka, Yoshimasa; Lin, Shu; Pisarski, Robert D.
  • Journal of High Energy Physics, Vol. 2015, Issue 10
  • DOI: 10.1007/JHEP10(2015)005

How wide is the transition to deconfinement?
journal, February 2011


A theory of scalar mesons
journal, May 2008


Z(N) interface tension in a hot SU(N) gauge theory
journal, September 1992


Degrees of freedom and the deconfining phase transition
journal, January 2002


α S from F π and renormalization group optimized perturbation theory
journal, October 2013


Equation of state for physical quark masses
journal, March 2010


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
  • DOI: 10.1142/S0218301315300076

Transition temperature in QCD
journal, September 2006


Is there still any T c mystery in lattice QCD? Results with physical masses in the continuum limit III
journal, September 2010

  • Borsányi, Szabolcs; Fodor, Zoltán; Hoelbling, Christian
  • Journal of High Energy Physics, Vol. 2010, Issue 9
  • DOI: 10.1007/JHEP09(2010)073

Chiral symmetry breaking in continuum QCD
journal, March 2015


Polyakov loop in 2 + 1 flavor QCD from low to high temperatures
journal, June 2016


Baryon number, strangeness, and electric charge fluctuations in QCD at high temperature
journal, April 2009


Suppression of the shear viscosity in a “semi”-quark-gluon plasma
journal, October 2008


Eigenvalue repulsion in an effective theory of SU(2) Wilson lines in three dimensions
journal, May 2008


Precision SU(3) lattice thermodynamics for a large temperature range
journal, July 2012

  • Borsányi, Sz.; Endrődi, G.; Fodor, Z.
  • Journal of High Energy Physics, Vol. 2012, Issue 7
  • DOI: 10.1007/JHEP07(2012)056

Deconfining phase transition as a matrix model of renormalized Polyakov loops
journal, August 2004


Three-loop HTLpt thermodynamics at finite temperature and chemical potential
journal, May 2014

  • Haque, Najmul; Bandyopadhyay, Aritra; Andersen, Jens O.
  • Journal of High Energy Physics, Vol. 2014, Issue 5
  • DOI: 10.1007/JHEP05(2014)027

Is There a Flavor Hierarchy in the Deconfinement Transition of QCD?
journal, November 2013


QCD Phase Transition with Chiral Quarks and Physical Quark Masses
journal, August 2014


The QCD transition temperature: Results with physical masses in the continuum limit
journal, November 2006


Equation of State for the SU(3) Gauge Theory
journal, December 1995


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    text, January 2018

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    • DOI: 10.15120/gsi-2019-00689