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Title: Spontaneous flavor and parity breaking with Wilson fermions

Abstract

We discuss the phase diagram of Wilson fermions in the m{sub 0}{minus}g{sup 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{close_quote}s conjecture. We show that they are in fact consistent with the presence of a flavor-parity broken {open_quotes}Aoki phase.{close_quotes} 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{sub 0}{approximately}a{sup 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. {copyright} {ital 1998} {ital The American Physical Society}

Authors:
Publication Date:
OSTI Identifier:
658518
Resource Type:
Journal Article
Journal Name:
Physical Review, D
Additional Journal Information:
Journal Volume: 58; Journal Issue: 7; Other Information: PBD: Oct 1998
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; PHASE DIAGRAMS; FERMIONS; QUANTUM CHROMODYNAMICS; SYMMETRY BREAKING; FLAVOR; PARITY; LATTICE FIELD THEORY; CHIRAL SYMMETRY; LAGRANGIAN FUNCTION; GOLDSTONE BOSONS; MASSLESS PARTICLES; PIONS

Citation Formats

Sharpe, S, and Singleton, R. , Jr. Spontaneous flavor and parity breaking with Wilson fermions. United States: N. p., 1998. Web. doi:10.1103/PhysRevD.58.074501.
Sharpe, S, & Singleton, R. , Jr. Spontaneous flavor and parity breaking with Wilson fermions. United States. doi:10.1103/PhysRevD.58.074501.
Sharpe, S, and Singleton, R. , Jr. Thu . "Spontaneous flavor and parity breaking with Wilson fermions". United States. doi:10.1103/PhysRevD.58.074501.
@article{osti_658518,
title = {Spontaneous flavor and parity breaking with Wilson fermions},
author = {Sharpe, S and Singleton, R. , Jr.},
abstractNote = {We discuss the phase diagram of Wilson fermions in the m{sub 0}{minus}g{sup 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{close_quote}s conjecture. We show that they are in fact consistent with the presence of a flavor-parity broken {open_quotes}Aoki phase.{close_quotes} 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{sub 0}{approximately}a{sup 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. {copyright} {ital 1998} {ital The American Physical Society}},
doi = {10.1103/PhysRevD.58.074501},
journal = {Physical Review, D},
number = 7,
volume = 58,
place = {United States},
year = {1998},
month = {10}
}