Angular momentum mixing in single flavor color superconductivity with transverse pairing

Because of the equal strength of the pairing potential mediated by one-gluon exchange for all partial waves to the leading order QCD running coupling constant and the nonlinearity of the gap equation, the non-spherical pairing in single flavor color superconductivity (CSC) cannot be restricted in a single non-s-wave channel and the mixing among different angular momenta will occur. In this paper, we examine the angular momentum mixing in single flavor CSC of massless quarks with transverse pairing, in which the pairing quarks have opposite helicity. We find that the free energy of all non-spherical pairing states are lowered by angular momentum mixing compared with that contain p-wave only, though the amount of the free energy drop is numerically small. Consequently the most stable pairing state in the ultra-relativistic limit remains the spherical color-spin-locked state (CSL).