Chiral matrix model of the semiQGP 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, m _{qk} . In addition, at a nonzero temperature T it is necessary to add a new term, ~ m _{qk} T ^{2} . 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, ηmore »
 Authors:
 Brookhaven National Lab. (BNL), Upton, NY (United States). Dept. of Physics
 Brookhaven National Lab. (BNL), Upton, NY (United States). RIKEN Research Center
 Publication Date:
 Research Org.:
 Brookhaven National Laboratory (BNL), Upton, NY (United States)
 Sponsoring Org.:
 USDOE Office of Under Secretary for Science (S4)
 OSTI Identifier:
 1338599
 Alternate Identifier(s):
 OSTI ID: 1286304
 Report Number(s):
 BNL1132492016JA
Journal ID: ISSN 24700010; PRVDAQ; R&D Project: KB0301020; KB0301020; TRN: US1701735
 Grant/Contract Number:
 SC0012704
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physical Review D
 Additional Journal Information:
 Journal Volume: 94; Journal Issue: 3; Journal ID: ISSN 24700010
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; SemiQuark Gluon Plasma; QCD
Citation Formats
Pisarski, Robert D., and Skokov, Vladimir V. Chiral matrix model of the semiQGP 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 semiQGP in QCD. United States. doi:10.1103/PhysRevD.94.034015.
Pisarski, Robert D., and Skokov, Vladimir V. Mon .
"Chiral matrix model of the semiQGP 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 semiQGP 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 = {Mon Aug 08 00:00:00 EDT 2016},
month = {Mon Aug 08 00:00:00 EDT 2016}
}
Web of Science

Cited by 4

Spectrum of the QCD Dirac operator and chiral random matrix theory
We argue that the spectrum of the QCD Dirac operator near zero virtuality can be described by random matrix theory. As in the case of the classical random matrix ensembles of Dyson we have three different cases: the chiral orthogonal ensemble, the chiral unitary ensemble, and the chiral symplectic ensemble. They correspond to gauge groups SU(2) in the fundamental representation, SU([ital N][sub [ital c]]), [ital N][sub [ital c]][ge]3 in the fundamental representation, and nonAbelian gauge groups SU([ital N][sub [ital c]]) for all [ital N][sub [ital c]] with fermions in the adjoint representation, respectively. The joint probability density reproduces LeutwylerSmilga summore » 
Twoflavor lattice QCD in the {epsilon} regime and chiral random matrix theory
The lowlying eigenvalue spectrum of the QCD Dirac operator in the {epsilon} regime is expected to match with that of chiral random matrix theory (ChRMT). We study this correspondence for the case including sea quarks by performing twoflavor QCD simulations on the lattice. Using the overlap fermion formulation, which preserves exact chiral symmetry at finite lattice spacings, we push the sea quark mass down to {approx}3 MeV on a 16{sup 3}x32 lattice at a lattice spacing a{approx_equal}0.11 fm. We compare the lowlying eigenvalue distributions and find a good agreement with the analytical predictions of ChRMT. By matching the lowestlying eigenvaluemore » 
Chiral random matrix theory for twocolor QCD at high density
We identify a nonHermitian chiral random matrix theory that corresponds to twocolor QCD at high density. We show that the partition function of the random matrix theory coincides with the partition function of the finitevolume effective theory at high density, and that the LeutwylerSmilgatype spectral sum rules of the random matrix theory are identical to those derived from the effective theory. The microscopic Dirac spectrum of the theory is governed by the BCS gap, rather than the conventional chiral condensate. We also show that with a different choice of a parameter the random matrix theory yields the effective partition functionmore » 
Lattice QCD at High Temperature and the QGP
We review recent progress in studies of bulk thermodynamics of strongly interacting matter, present results on the QCD equation of state and discuss the status of studies of the phase diagram at nonvanishing quark chemical potential.