Angular Momentum Mixing in a Non-spherical Color Superconductor

We study the angular momentum mixing effects in the color superconductor with non-spherical pairing. We first clarify the concept of the angular momentum mixing with a toy model for non-relativistic and spinless fermions. Then we derive the gap equation for the polar phase of dense QCD by minimizing the CJT free energy. The solution of the gap equation consists of all angular momentum partial waves of odd parity. The corresponding free energy is found to be lower than that reported in the literature with p-wave only.