Quark masses, the Dashen phase, and gauge field topology

Understand

The CP violating Dashen phase in QCD is predicted by chiral perturbation theory to occur when the up-down quark mass difference becomes sufficiently large at fixed down-quark mass.

• Before reaching this phase, all physical hadronic masses and scattering amplitudes are expected to behave smoothly with the up-quark mass, even as this mass passes through zero.
• In Euclidean space, the topological susceptibility of the gauge fields is positive at positive quark masses but diverges to negative infinity as the Dashen phase is approached.
• A zero in this susceptibility provides a tentative signal for the point where the mass of the up quark vanishes.