Inverse meson mass ordering in the color-flavor-locking phase of high-density QCD

We derive the effective Lagrangian for the low-energy massive meson excitations of the color-flavor-locking (CFL) phase of QCD with three flavors of light quarks. We compute the decay constants, the maximum velocities, and the masses of the mesons at large baryon chemical potential μ. The decay constants are linear in μ. The meson maximum velocities are close to that of sound. The meson masses in the CFL phase are significantly smaller than in the normal QCD vacuum and depend only on bare quark masses. The order of the meson masses is, to some extent, reversed compared to that in the QCD vacuum. In particular, the lightest particle is ${\mathrm{\eta }}^{\prime }$.