RGE solver for the complete dim-7 SMEFT interactions and its application to 0νββ decay

Abstract

Abstract We present an automatic renormalization group equations (RGEs) solver, D7RGESolver, designed for the precise numerical solution of one-loop RGEs of dimension-7 (dim-7) operators within the standard model effective field theory (SMEFT). This tool is capable of calculating the RGE effects of dim-5 and dim-7 SMEFT operators between any two scales above the electroweak scale. We take the nuclear neutrinoless double beta (0νββ) decay process as an example to appreciate the importance of the running effects in phenomenological studies. Our analysis demonstrates that 0νββ decay can constrain nearly all dim-7 SMEFT operators involving first-generation leptons that violate lepton number by two units, after accounting for RGE effects. Specifically, we have placed meaningful constraints on 55 dim-7 Wilson coefficients, compared to only 10 from a simple tree-level analysis. Certain operators exhibit much stricter constraints when RGE effects are included, especially for the operators that mix with neutrino mass operators. We provide a complete code documentation for D7RGESolver, along with examples of its usage and interfacing with external automated codes for calculating 0νββ decay. The D7RGESolver code is available at: Github: D7RGESolver

Keywords

• Baryon/Lepton Number Violation
• Renormalization Group
• SMEFT