Pion masses in 2-flavor QCD with $\eta$ condensation

Understand

We investigate some aspects of 2-flavor QCD with $m_u\not= m_d$ at low-energy, using the leading order chiral perturbation theory including anomaly effects.

• While nothing special happens at $m_u=0$ for the fixed $m_d\not=0$, 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.