RGE solver for the complete dim-7 SMEFT interactions and its application to $0\nu\beta\beta$ decay

TL;DR

This paper introduces D7RGESolver, an automated tool for solving one-loop RGEs of dimension-7 SMEFT operators, demonstrating its application to constraining operators via neutrinoless double beta decay analysis.

Contribution

The paper presents a new RGE solver for dim-7 SMEFT operators and applies it to analyze $0 uetaeta$ decay constraints, improving upon previous tree-level estimates.

Findings

RGE effects significantly tighten constraints on dim-7 operators.

D7RGESolver accurately computes RGE running for SMEFT operators.

Nearly all first-generation lepton-number-violating dim-7 operators are constrained.

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 ($0\nu\beta\beta$) decay process as an example to appreciate the importance of the running effects in phenomenological studies. Our analysis demonstrates that $0\nu\beta\beta$ 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 $0\nu\beta\beta$ decay. The D7RGESolver code is available at: \href{https://github.com/ZhaoXiang210/D7RGESolver}{Github: D7RGESolver}