Complete Two-loop Renormalization Group Equation of the Weinberg Operator

Abstract: We calculate the renormalization group equation (RGE) of the lepton-number-violating Weinberg operator with the particle content of the Standard Model (SM), thus completing the set of two-loop RGEs of the SM effective field theory up to dimension 5. We identify new diagrams that could increase the rank of the Wilson coefficient of the Weinberg operator, and we calculate the complete two-loop RGE for the neutrino mass eigenvalues and leptonic mixing matrix. We also briefly discuss some phenomenological implications of the RGEs.