Leptonic Unitarity Triangles and Effective Mass Triangles of the Majorana Neutrinos

TL;DR

This paper visualizes the shapes of leptonic unitarity triangles and effective mass triangles for Majorana neutrinos, exploring their geometric properties and connections to neutrino oscillations, phases, and lepton-number-violating decays.

Contribution

It presents the first graphical depiction of Dirac and Majorana unitarity triangles based on current neutrino data and analyzes their implications for neutrino properties and decays.

Findings

Real shapes of unitarity triangles are shown for the first time.

Connections between triangles and neutrino-antineutrino oscillations are explored.

Relations between triangles, Majorana phases, and lepton-number-violating decays are illustrated.

Abstract

Given the best-fit results of six neutrino oscillation parameters, we plot the Dirac and Majorana unitarity triangles (UTs) of the 3\times 3 lepton flavor mixing matrix to show their real shapes for the first time. The connections of the Majorana UTs with neutrino-antineutrino oscillations and neutrino decays are explored, and the possibilities of right or isosceles UTs are discussed. In the neutrino mass limit of m_1 \to 0 or m_3 \to 0, which is allowed by current experimental data, we show how the six triangles formed by the effective Majorana neutrino masses \langle m\rangle_{\alpha\beta} (for \alpha, \beta = e, \mu, \tau) and their corresponding component vectors look like in the complex plane. The relations of such triangles to the Majorana phases and to the lepton-number-violating decays H^{++} \to \alpha^+ \beta^+ in the type-II seesaw mechanism are also illustrated.