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

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.