Geometry of the effective Majorana neutrino mass in the neutrinoless double-beta decay

TL;DR

This paper introduces a geometric 'coupling-rod' diagram to visualize and analyze the effective Majorana neutrino mass relevant for neutrinoless double-beta decay, clarifying the effects of neutrino parameters.

Contribution

The novel 'coupling-rod' diagram provides an intuitive geometric approach to understanding the effective Majorana neutrino mass and its dependence on neutrino parameters.

Findings

Allows easy determination of maximum and minimum effective masses.

Remains applicable even with new physics contributions.

Extensible to other lepton-number-violating processes.

Abstract

The neutrinoless double-beta ($0\nu\beta\beta$) decay is a unique process to identify the Majorana nature of massive neutrinos, and its rate depends on the size of the effective Majorana neutrino mass $\langle m\rangle_{ee}$. We put forward a novel "coupling-rod" diagram to describe $\langle m\rangle_{ee}$ in the complex plane, by which the effects of the neutrino mass ordering and CP-violating phases on $\langle m\rangle_{ee}$ are intuitively understood. We show that this geometric language allows us to easily obtain the maximum and minimum of $|\langle m\rangle_{ee}|$. It remains usable even if there is a kind of new physics contributing to $\langle m\rangle_{ee}$, and it can also be extended to describe the effective Majorana masses $\langle m\rangle_{e\mu}$, $\langle m\rangle_{e\tau}$, $\langle m\rangle_{\mu\mu}$, $\langle m\rangle_{\mu\tau}$ and $\langle m\rangle_{\tau\tau}$ which may appear in some other lepton-number-violating processes.