One-loop Renormalization of the Type-I Seesaw Model in the Modified Minimal-subtraction Scheme

TL;DR

This paper performs a comprehensive one-loop renormalization of the type-I seesaw model within the $ar{MS}$ scheme, providing detailed calculations of corrections and renormalization-group equations to facilitate precise testing of the model.

Contribution

It offers the first complete one-loop renormalization and RG equations for the type-I seesaw model, including explicit counterterms and gauge calculations.

Findings

Derived explicit one-loop counterterms for leptonic fields and parameters.

Established RG equations for neutrino masses, mixing angles, and CP phases.

Analyzed the impact of heavy Majorana neutrinos on SM parameter renormalization.

Abstract

Extending the Standard Model (SM) with three right-handed neutrinos, the type-I seesaw model serves as the simplest and most natural scenario to successfully explain both tiny neutrino masses and the baryon number asymmetry in the Universe. In this paper, we perform a complete one-loop renormalization of the type-I seesaw model in the modified minimal-subtraction ($\overline{\rm MS}$) scheme. The one-loop self-energy corrections of charged leptons and Majorana neutrinos are calculated in the $R_\xi^{}$ gauge, and the explicit expressions of all the counterterms for wave functions, fermion masses and the leptonic flavor mixing matrix are given. Furthermore, adopting the Euler-like parametrization of the $6\times 6$ unitary leptonic flavor mixing matrix, we derive one-loop renormalization-group equations for all the physical parameters in the $\overline{\rm MS}$ scheme, including neutrino masses, mixing angles and CP-violating phases. The modification of the one-loop renormalization of the original SM parameters due to the presence of heavy Majorana neutrinos is investigated as well. In this way, we provide a self-consistent theoretical framework to thoroughly test the type-I seesaw model at the one-loop level with future precision data.