Complete Two-loop Renormalization Group Equation of the Weinberg Operator

TL;DR

This paper derives the complete two-loop renormalization group equations for the Weinberg operator within the Standard Model, providing essential tools for understanding neutrino mass evolution and related phenomenology.

Contribution

It presents the first full two-loop RGE calculation for the Weinberg operator, including new diagrams affecting the Wilson coefficient and neutrino parameters.

Findings

Complete two-loop RGE for the Weinberg operator derived

Identification of new diagrams influencing Wilson coefficient

Implications for neutrino mass and mixing evolution

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.