Spontaneous flavor and parity breaking with Wilson fermions
Abstract
We discuss the phase diagram of Wilson fermions in the m_{0}g^{2} plane for twoflavor 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 flavorparity 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 nonzero lattice spacing: (1) there is an Aoki phase of width ∆m_{0}~a^{3} with two massless Goldstone pions; (2) there is no symmetry breaking, and all three pions have an equal nonvanishing 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 flavorparity breaking condensate within the Aoki phase. Our analysis also applies for nonperturbatively improved Wilson fermions.
 Publication:

Physical Review D
 Pub Date:
 October 1998
 DOI:
 10.1103/PhysRevD.58.074501
 arXiv:
 arXiv:heplat/9804028
 Bibcode:
 1998PhRvD..58g4501S
 Keywords:

 11.15.Ha;
 11.30.Hv;
 11.30.Rd;
 12.39.Fe;
 Lattice gauge theory;
 Flavor symmetries;
 Chiral symmetries;
 Chiral Lagrangians;
 High Energy Physics  Lattice;
 High Energy Physics  Phenomenology
 EPrint:
 22 pages, LaTeX, 5 figures (added several references and a comment)