Leptonic Unitarity Triangles and Effective Mass Triangles of the Majorana Neutrinos

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_{αβ} (for α, β= e, μ, τ) 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 α^+ β^+ in the type-II seesaw mechanism are also illustrated.

18 pages, 4 figures, more discussions added. Invited contribution to the Special Issue on Neutrino Oscillations for celebrating the Nobel Prize in Physics 2015 (Nucl. Phys. B in press)

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Cited by in corpus (15)

• Flavor structures of charged fermions and massive neutrinos
• A review of mu-tau flavor symmetry in neutrino physics
• The minimal seesaw and leptogenesis models
• Type-II Seesaw Scalar Triplet Model at a 100 TeV $pp$ Collider: Discovery and Higgs Portal Coupling Determination
• Analytical approximations for matter effects on CP violation in the accelerator-based neutrino oscillations with E \lesssim 1 GeV
• Renormalization-Group Equations of Neutrino Masses and Flavor Mixing Parameters in Matter
• Radiative decays of charged leptons as constraints of unitarity polygons for active-sterile neutrino mixing and CP violation
• Looking into Analytical Approximations for Three-flavor Neutrino Oscillation Probabilities in Matter
• Sum rules and asymptotic behaviors of neutrino mixing in dense matter
• Neutrino mixing, interval matrices and singular values
• Leptonic unitarity triangles: RGE running effects and $\mu$-$\tau$ reflection symmetry breaking
• Connecting Leptonic Unitarity Triangle to Neutrino Oscillation with CP Violation in Vacuum and in Matter
• Distinguishing between the twin $b$-flavored unitarity triangles on a circular arc
• Neutrino mass observables and non-Hermitian version of Type-I seesaw model
• Connecting Majorana phases to the Geometric Parameters of Majorana Unitarity Triangle in a model of Neutrino Mass Matrix