Pion masses in 2-flavor QCD with $η$ condensation

Sinya Aoki; Michael Creutz

doi:10.1103/PhysRevLett.112.141603

paper

Pion masses in 2-flavor QCD with $η$ condensation

arXiv:1402.1837 · doi:10.1103/PhysRevLett.112.141603

Abstract

We investigate some aspects of 2-flavor QCD with $m_{u} \neq = m_{d}$ at low-energy, using the leading order chiral perturbation theory including anomaly effects. While nothing special happens at $m_{u} = 0$ for the fixed $m_{d} \neq = 0$ , the neutral pion mass becomes zero at two critical values of $m_{u}$ , 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 ChPT diverges at these two critical points. We briefly discuss a possibility that $m_{u} = 0$ can be defined by the vanishing the "topological susceptibility. We finally analyze the case of $m_{u} = m_{d} = m$ with $θ = π$ , which is equivalent to $m_{u} = - m_{d} = - m$ 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 $m_{π}^{2} = O (m^{2})$ , which, however, is shown to be consistent with the chiral Ward-Takahashi identities.

10 pages, 2 figures

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Quark masses, the Dashen phase, and gauge field topology

Pion masses in 2-flavor QCD with η condensation

Abstract

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Pion masses in 2-flavor QCD with $η$ condensation