Pseudoscalar Masses in the Effective Theory for Color-Flavor Locking in high density QCD

The constants of the effective action describing the massless modes in the color-flavor-locking phase of QCD have been recently evaluated at high density. Values of the pseudoscalar masses for nonvanishing quark masses have also been given. The calculated values show however a puzzling feature: when $m_u=m_d=0$ and $m_s≠0$ all the goldstones remain massless. We show that an additional invariant is present which avoids this feature. We costruct this invariant and discuss the emerging mass pattern for the pseudogoldstones. This provides for a complete scheme for the pseudogoldstone masses in the color-flavor-locking phase of QCD.