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

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 $⟨m{⟩}_{ee}$. We put forward a novel "coupling-rod" diagram to describe $⟨m{⟩}_{ee}$ in the complex plane, by which the effects of the neutrino mass ordering and CP-violating phases on $⟨m{⟩}_{ee}$ are intuitively understood. We show that this geometric language allows us to easily obtain the maximum and minimum of $|⟨m{⟩}_{ee}|$. It remains usable even if there is a kind of new physics contributing to $⟨m{⟩}_{ee}$, and it can also be extended to describe the effective Majorana masses $⟨m{⟩}_{e\mu }$, $⟨m{⟩}_{e\tau }$, $⟨m{⟩}_{\mu \mu }$, $⟨m{⟩}_{\mu \tau }$ and $⟨m{⟩}_{\tau \tau }$ which may appear in some other lepton-number-violating processes.

Comments: PDFLaTex 10 pages, 3 figures. Minor changes, to appear in Chinese Physcs C