Electroweak Physics for Color Superconductivity

We construct the effective theories describing the electroweak interactions for the low energy excitations associated with the color superconductive phases of QCD at high matter density. The main result, for the 3 flavor case, is that the quasiparticle Goldstone boson $\pi^0$ decay into two physical massless photons is identical to the zero density case once we use the new Goldstone decay constant and the modified electric charge $\widetilde{e}=e \cos\theta$, with $\tan\theta =2e/\sqrt{3}g_s$ and $g_s$ the strong coupling constant. For 2 flavors we find that the coupling of the quarks to the neutral vector boson $Z^0$ is modified with respect to the zero density case. We finally point out possible applications of our result to the physics of compact objects.