Spontaneous Flavor and Parity Breaking with Wilson Fermions

We discuss the phase diagram of Wilson fermions in the $m_0$--$g^2$ plane for two-flavor QCD. We argue that, as originally suggested by Aoki, there is a phase in which flavor and parity are spontaneously broken. Recent numerical results on the spectrum of the overlap Hamiltonian have been interpreted as evidence against Aoki's conjecture. We show that they are in fact consistent with the presence of a flavor-parity broken ``Aoki phase''. We also show how, as the continuum limit is approached, one can study the lattice theory using the continuum chiral Lagrangian supplemented by additional terms proportional to powers of the lattice spacing. We find that there are two possible phase structures at non-zero lattice spacing: (1) there is an Aoki phase of width $\Delta m_0 \sim a^3$ with two massless Goldstone pions; (2) there is no symmetry breaking, and all three pions have an equal non-vanishing mass of order $a$. Present numerical evidence suggests that the former option is realized for Wilson fermions. Our analysis then predicts the form of the pion masses and the flavor-parity breaking condensate within the Aoki phase. Our analysis also applies for non-perturbatively improved Wilson fermions.Comment: 22 pages, LaTeX, 5 figures (added several references and a comment

Two-dimensional Lattice Gross-Neveu Model with Wilson Fermion Action at Finite Temperature and Chemical Potential

We investigate the phase structure of the two-dimensional lattice Gross-Neveu model formulated with the Wilson fermion action to leading order of 1/N expansion. Structural change of the parity-broken phase under the influence of finite temperature and chemical potential is studied. The connection between the lattice phase structure and the chiral phase transition of the continuum theory is clarified.Comment: 42 pages, 20 EPS figures, using REVTe

Nucleon-nucleon interactions via Lattice QCD: Methodology --HAL QCD approach to extract hadronic interactions in lattice QCD--

We review the potential method in lattice QCD, which has recently been proposed to extract nucleon-nucleon interactions via numerical simulations. We focus on the methodology of this approach by emphasizing the strategy of the potential method, the theoretical foundation behind it, and special numerical techniques. We compare the potential method with the standard finite volume method in lattice QCD, in order to make pros and cons of the approach clear. We also present several numerical results for the nucleon-nucleon potentials.Comment: 12 pages, 10 figure

Finite-Temperature Phase Structure of Lattice QCD with the Wilson Quark Action for Two and Four Flavors

We present further analyses of the finite-temperature phase structure of lattice QCD with the Wilson quark action based on spontaneous breakdown of parity-flavor symmetry. Results are reported on (i) an explicit demonstration of spontaneous breakdown of parity-flavor symmetry beyond the critical line, (ii) phase structure and order of chiral transition for the case of $N_f=4$ flavors, and (iii) approach toward the continuum limit.Comment: Poster presented at LATTICE96(finite temperature); 4 pages, Latex, uses espcrc2 and epsf, seven ps figures include

One loop renormalization for the axial Ward-Takahashi identity in Domain-wall QCD

We calculate one-loop correction to the axial Ward-Takahashi identity given by Furman and Shamir in domain-wall QCD. It is shown perturbatively that the renormalized axial Ward-Takahashi identity is satisfied without fine tuning and the ``conserved'' axial current receives no renormalization, giving $Z_A=1$. This fact will simplify the calculation of the pion decay constant in numerical simulations since the decay constant defined by this current needs no lattice renormalization factor.Comment: 16 pages, 3 axodraw.sty figure

Domain Wall Fermions in Quenched Lattice QCD

We study the chiral properties and the validity of perturbation theory for domain wall fermions in quenched lattice QCD at beta=6.0. The explicit chiral symmetry breaking term in the axial Ward-Takahashi identity is found to be very small already at Ns=10, where Ns is the size of the fifth dimension, and its behavior seems consistent with an exponential decay in Ns within the limited range of Ns we explore. From the fact that the critical quark mass, at which the pion mass vanishes as in the case of the ordinary Wilson-type fermion, exists at finite Ns, we point out that this may be a signal of the parity broken phase and investigate the possible existence of such a phase in this model at finite Ns. The rho and pi meson decay constants obtained from the four-dimensional local currents with the one-loop renormalization factor show a good agreement with those obtained from the conserved currents

The Weakly Coupled Gross-Neveu Model with Wilson Fermions

The nature of the phase transition in the lattice Gross-Neveu model with Wilson fermions is investigated using a new analytical technique. This involves a new type of weak coupling expansion which focuses on the partition function zeroes of the model. Its application to the single flavour Gross-Neveu model yields a phase diagram whose structure is consistent with that predicted from a saddle point approach. The existence of an Aoki phase is confirmed and its width in the weakly coupled region is determined. Parity, rather than chiral symmetry breaking naturally emerges as the driving mechanism for the phase transition.Comment: 15 pages including 1 figur

Finite-temperature chiral transitions in QCD with the Wilson quark action

We investigate the finite-temperature phase structure and the scaling of the chiral condensate in lattice QCD with two degenerate light quarks, using a renormalization group improved gauge action and the Wilson quark action. We obtain a phase diagram which is consistent with that from the parity-flavor breaking scenario. The scaling relation for the chiral condensate assuming the critical exponents and the scaling function of the three dimensional O(4) model is remarkably satisfied for a wide range of parameters. This indicates that the chiral transition in two flavor QCD is of second order in the continuum limit.Comment: LaTeX, 3 pages, 4 EPS figures, Talk presented at LATTICE97 (finite temperature