Wigner-like Parametrization of Canonical Seesaw Models

TL;DR

This paper introduces a Wigner parametrization for unitary matrices to describe canonical seesaw models, capturing the hierarchy between electroweak and seesaw scales with small angles and connecting it to existing parametrizations.

Contribution

It develops a novel Wigner parametrization framework for canonical seesaw models, clarifying parameter hierarchies and linking to previous parametrizations.

Findings

Wigner parametrization effectively describes hierarchy in seesaw models.

Small rotation angles approximate the scale separation between electroweak and seesaw.

Established connection between Wigner parametrization and existing literature.

Abstract

In this paper, we introduce the Wigner parametrization of unitary matrices and then apply it to the full description of canonical seesaw models, which extend the Standard Model with three right-handed neutrino singlets and account simultaneously for tiny Majorana neutrino masses and the baryon number asymmetry in the Universe. In the Wigner parametrization, the strong hierarchy between the electroweak scale $\Lambda^{}_{\rm EW} \approx 10^2~{\rm GeV}$ and the seesaw scale $\Lambda^{}_{\rm SS} \approx 10^{14}~{\rm GeV}$ is generally captured by three small rotation angles $\{\vartheta^{}_1, \vartheta^{}_2, \vartheta^{}_3\} \approx {\cal O}(\Lambda^{}_{\rm EW}/\Lambda^{}_{\rm SS})$, and all the remaining parameters reside in four $3\times 3$ unitary matrices. The connection between the Wigner parametrization and those in the literature is also established.