The Grimus-Neufeld model [1] is an extension of the Standard Model (SM) of particle physics providing a mechanism of neutrino mass generation. The addition of neutrino masses to the SM also introduces mixing between neutrinos and there is a corresponding mixing matrix, known as the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix [2, 3]. This matrix has to be measured, however, to connect theory and experiment, it is needed to take care of ultraviolet (UV) divergences arising already in 1-loop calculations. With the procedure of renormalization it is possible to absorb all the UV divergences by adding counterterms to the Lagrangian of the theory. The PMNS matrix is no exception and one has to define a corresponding counterterm to ensure the finiteness of physical quantities. However, there is freedom in choosing a renormalization scheme and a few options are already available in literature [4, 5, 6]. One of the available schemes is gauge dependent, a feature one usually tries to avoid, while the other is slightly unconventional.
In this work we define a new scheme of fermion mixing renormalization and as an example we use the Grimus-Neufeld model. The new renormalization scheme provides explicitly gauge independent counterterms for the mixing matrix while mostly keeping in tact the usual definitions of renormalization constants. We have already checked some properties of the new scheme by explicit calculation in the Grimus-Neufeld model, but there still are outstanding tasks, for example, checking whether all of the UV divergences are correctly subtracted in the Wlv-vertex.