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Title: Two-flavor QCD phases and condensates at finite isospin chemical potential

Abstract

We study the phase structure and condensates of two-flavor QCD at finite isospin chemical potential in the framework of a confining, Dyson-Schwinger equation model. We find that the pion superfluidity phase is favored at high enough isospin chemical potential. A new gauge-invariant mixed quark-gluon condensate induced by isospin chemical potential is proposed based on operator product expansion. We investigate the sign and magnitude of this new condensate and show that it is an important condensate in QCD sum rules at finite isospin density.

Authors:
;  [1]
  1. Department of Physics, Peking University, Beijing 100871 (China) and CCAST (World Laboratory), Post Office Box 8730, Beijing 100080 (China)
Publication Date:
OSTI Identifier:
20995160
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. C, Nuclear Physics; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevC.75.035201; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CONDENSATES; DENSITY; GAUGE INVARIANCE; GLUON CONDENSATION; ISOSPIN; OPERATOR PRODUCT EXPANSION; PIONS; POTENTIALS; QUANTUM CHROMODYNAMICS; QUARKS; SUM RULES; SUPERFLUIDITY

Citation Formats

Zhang Zhao, and Liu Yuxin. Two-flavor QCD phases and condensates at finite isospin chemical potential. United States: N. p., 2007. Web. doi:10.1103/PHYSREVC.75.035201.
Zhang Zhao, & Liu Yuxin. Two-flavor QCD phases and condensates at finite isospin chemical potential. United States. doi:10.1103/PHYSREVC.75.035201.
Zhang Zhao, and Liu Yuxin. Thu . "Two-flavor QCD phases and condensates at finite isospin chemical potential". United States. doi:10.1103/PHYSREVC.75.035201.
@article{osti_20995160,
title = {Two-flavor QCD phases and condensates at finite isospin chemical potential},
author = {Zhang Zhao and Liu Yuxin},
abstractNote = {We study the phase structure and condensates of two-flavor QCD at finite isospin chemical potential in the framework of a confining, Dyson-Schwinger equation model. We find that the pion superfluidity phase is favored at high enough isospin chemical potential. A new gauge-invariant mixed quark-gluon condensate induced by isospin chemical potential is proposed based on operator product expansion. We investigate the sign and magnitude of this new condensate and show that it is an important condensate in QCD sum rules at finite isospin density.},
doi = {10.1103/PHYSREVC.75.035201},
journal = {Physical Review. C, Nuclear Physics},
number = 3,
volume = 75,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}
  • We study the phase diagram of two-flavor QCD at imaginary chemical potentials in the chiral limit. To this end we compute order parameters for chiral symmetry breaking and quark confinement. The interrelation of quark confinement and chiral symmetry breaking is analyzed with a new order parameter for the confinement phase transition. We show that it is directly related to both the quark density as well as the Polyakov loop expectation value. Our analytical and numerical results suggest a close relation between the chiral and the confinement phase transition.
  • We simulate 2-flavor lattice QCD at finite isospin chemical potential {mu}{sub I}, for temperatures close to the finite temperature transition from hadronic matter to a quark-gluon plasma. The {mu}{sub I} dependence of the transition coupling is observed and used to estimate the decrease in the transition temperature with increasing {mu}{sub I}. These simulations are performed on an 8{sup 3}x4 lattice at three different quark masses. Our estimate of the magnitude of the fluctuations of the phase of the fermion determinant at small quark-number chemical potential {mu}, suggest that the position of the small {mu} and small {mu}{sub I} transitions shouldmore » be the same for {mu}{sub I}=2{mu}, and we argue that the nature of these transitions should be the same. For all {mu}{sub I}<m{sub {pi}} the smoothness of these transitions and the values of the Binder cumulant B{sub 4}, indicate that these transitions are mere crossovers, and show no sign of a critical endpoint corresponding to that expected at finite {mu}. This suggests that this finite {mu} critical endpoint, if it exists, lies at {mu}>m{sub {pi}}/2 over the considered range of quark masses. For {mu}{sub I}>m{sub {pi}} and a small isospin (I{sub 3}) breaking term {lambda}, we do find evidence of a critical endpoint which would indicate that, for {lambda}=0, there is a tricritical point on the phase boundary where the pion condensate evaporates, where this phase transition changes from second to first-order.« less
  • We present results of a simulation of two flavor QCD on a 16{sup 3}x4 lattice using p4-improved staggered fermions with bare quark mass m/T=0.4. Derivatives of the thermodynamic grand canonical partition function Z(V,T,{mu}{sub u},{mu}{sub d}) with respect to chemical potentials {mu}{sub u,d} for different quark flavors are calculated up to sixth order, enabling estimates of the pressure and the quark number density as well as the chiral condensate and various susceptibilities as functions of {mu}{sub q}=({mu}{sub u}+{mu}{sub d})/2 via Taylor series expansion. Furthermore, we analyze baryon as well as isospin fluctuations and discuss the relation between the radius of convergencemore » of the Taylor series and the chiral critical point in the QCD phase diagram. We argue that bulk thermodynamic observables do not, at present, provide direct evidence for the existence of a chiral critical point in the QCD phase diagram. Results are compared to high temperature perturbation theory as well as a hadron resonance gas model.« less
  • Isospin density and thermal corrections for several condensates are discussed, at the one-loop level, in the frame of chiral dynamics with pionic degrees of freedom. The evolution of such objects gives an additional insight into the condensed-pion phase transition that occurs basically when vertical bar {mu}{sub I} vertical bar>m{sub {pi}}, vertical bar {mu}{sub I} vertical bar being the isospin chemical potential. Calculations are done in both phases, showing a good agreement with lattice results for such condensates.
  • We present results for phase structure of lattice QCD with two degenerate flavors (N{sub f}=2) of Wilson quarks at finite temperature T and small baryon chemical potential {mu}{sub B}. Using the imaginary chemical potential for which the fermion determinant is positive, we perform simulations at points where the ratios of pseudoscalar meson mass to the vector meson mass m{sub {pi}}/m{sub {rho}} are between 0.943(3) and 0.899(4) as well as in the quenched limit. By analytic continuation to real quark chemical potential {mu}, we obtain the transition temperature as a function of small {mu}{sub B}. We attempt to determine the naturemore » of transition at imaginary chemical potential by histogram, Monte Carlo (MC) history, and finite size scaling. In the infinite heavy quark limit, the transition is of first order. At intermediate values of quark mass m{sub q} corresponding to the ratio of m{sub {pi}}/m{sub {rho}} in the range from 0.943(3) to 0.899(4) at a{mu}{sub I}=0.24, the MC simulations show the absence of phase transition.« less