Pion masses in two-flavor QCD with η condensation.

Abstract

We investigate some aspects of two-flavor QCD with mu≠md at low energy, using the leading order chiral perturbation theory including anomaly effects. While nothing special happens at mu=0 for the fixed md≠0, the neutral pion mass becomes zero at two critical values of mu, between which the neutral pion field condenses, leading to a spontaneously CP broken phase, the so-called Dashen phase. We also show that the "topological susceptibility" in the chiral perturbation theory diverges at these two critical points. We briefly discuss a possibility that mu=0 can be defined by the vanishing the "topological susceptibility. We finally analyze the case of mu=md=m with θ=π, which is equivalent to mu=-md=-m with θ=0 by the chiral rotation. In this case, the η condensation occurs at small m, violating the CP symmetry spontaneously. Deep in the η condensation phase, three pions become Nambu-Goldstone bosons, but they show unorthodox behavior at small m that mπ2=O(m2), which, however, is shown to be consistent with the chiral Ward-Takahashi identities.