Generalised Casas-Ibarra Parametrisation for Majorana Neutrino Masses

TL;DR

This paper introduces a comprehensive extension of the Casas-Ibarra parametrisation that universally applies to Majorana neutrino mass models, simplifying analysis and enabling classification of various neutrino mass mechanisms.

Contribution

It develops a unified, minimal framework for parametrising Yukawa sectors in Majorana neutrino models, accommodating additional degrees of freedom and classifying models by mass matrix structure.

Findings

Provides explicit parametrisation formulas for known models

Classifies neutrino mass models into tree-level and loop-level categories

Simplifies analytical and numerical analysis of neutrino mass models

Abstract

We present a simple and broadly applicable extension of the Casas-Ibarra parametrisation that captures the structure of all Majorana neutrino mass models. Building directly on the original formulation, our approach naturally accommodates additional degrees of freedom and provides a unified, minimal framework for parametrising the Yukawa sector. It significantly simplifies both analytical treatments and numerical scans, and can be universally applied to any Majorana neutrino mass model, regardless of the underlying dynamics. The approach also offers a unified framework for classifying neutrino mass models according to the structure of the neutrino mass matrix, which naturally motivates the proposal of an extended version of the Scotogenic Model. This classification scheme yields tree-level (loop-level) representative models: the seesaw (Scotogenic Model), the linear seesaw (the Generalised Scotogenic Model), and the linear plus inverse seesaw (the Extended Scotogenic Model). We provide ready-to-use explicit expressions for several well-known scenarios, including the Zee model where one of the Yukawa matrices is antisymmetric.