Complete One-loop Matching of the Type-I Seesaw Model onto the Standard Model Effective Field Theory

TL;DR

This paper performs a comprehensive one-loop matching of the type-I seesaw model onto the Standard Model Effective Field Theory, calculating Wilson coefficients for relevant operators to facilitate low-energy phenomenological studies.

Contribution

It provides the first complete one-loop matching of the type-I seesaw model onto SMEFT, identifying 31 key dimension-six operators and computing their Wilson coefficients.

Findings

Identified 31 relevant dimension-six operators in SMEFT from the seesaw model.

Computed Wilson coefficients up to order M^{-2} for these operators.

Discussed threshold corrections to Standard Model couplings and dimension-five operator.

Abstract

In this paper, we accomplish the complete one-loop matching of the type-I seesaw model onto the Standard Model Effective Field Theory (SMEFT), by integrating out three heavy Majorana neutrinos with the functional approach. It turns out that only 31 dimension-six operators (barring flavor structures and Hermitian conjugates) in the Warsaw basis of the SMEFT can be obtained, and most of them appear at the one-loop level. The Wilson coefficients of these 31 dimension-six operators are computed up to $\mathcal{O}\left( M^{-2}\right)$ with $M$ being the mass scale of heavy Majorana neutrinos. As the effects of heavy Majorana neutrinos are encoded in the Wilson coefficients of these higher-dimensional operators, a complete one-loop matching is useful to explore the low-energy phenomenological consequences of the type-I seesaw model. In addition, the threshold corrections to the couplings in the Standard Model and to the coefficient of the dimension-five operator are also discussed.