Sufficient and Necessary Conditions for CP Conservation in the Case of Degenerate Majorana Neutrino Masses

Abstract

In this paper, we carry out a systematic study of the sufficient and necessary conditions for CP conservation in the leptonic sector with massive Majorana neutrinos. In particular, the emphasis is placed on the number of CP-violating phases in the presence of a partial mass degeneracy (e.g., $m_1^{}=m_2^{}\ne m_3^{}$) or a complete mass degeneracy $m_1^{}=m_2^{}=m_3^{}$, where $m_i^{}$ (for $i=1,2,3$) stand for the masses of three ordinary neutrinos. In the canonical seesaw model with three right-handed neutrino singlets, CP-violating phases in the special case of a partial (e.g., $M_1^{}=M_2^{}\ne M_3^{}$) or complete (i.e., $M_1^{}=M_2^{}=M_3^{}$) mass degeneracy of three heavy Majorana neutrinos are also examined. In addition, we derive the renormalization-group equations of the weak-basis invariants in the effective theory with a general mass spectrum of Majorana neutrinos, to which the solutions establish the direct connection between CP violation at low- and high-energy scales.

arXiv comment28 pages, 2 tables, more discussions and references added, accepted for publication in Phys. Rev. D

References in corpus (48)

• Oscillating neutrinos and mu --> e, gamma
• The fate of hints: updated global analysis of three-flavor neutrino oscillations
• Leptogenesis
• Resonant Leptogenesis
• CP Violation and Baryogenesis due to Heavy Majorana Neutrinos
• Electroweak-Scale Resonant Leptogenesis
• Cosmological Sign of Neutrino CP Violation
• Renormalization of the Neutrino Mass Operator
• Running Neutrino Masses, Mixings and CP Phases: Analytical Results and Phenomenological Consequences
• Running Neutrino Mass Parameters in See-Saw Scenarios
• Renormalization Group Equations for Seesaw Neutrino Masses
• Flavor structures of charged fermions and massive neutrinos
• Large Mixing Angle MSW and Atmospheric Neutrinos from Single Right-Handed Neutrino Dominance and U(1) Family Symmetry
• Neutrino Mass Operator Renormalization Revisited
• Neutrino Phenomenology -- the case of two right handed neutrinos
• Leptonic CP violation
• Current unknowns in the three neutrino framework
• Constructing the large mixing angle MNS matrix in see-saw models with right-handed neutrino dominance
• Flavour Covariant Transport Equations: an Application to Resonant Leptogenesis
• Baryogenesis from the weak scale to the grand unification scale
• A Bridge between CP violation at Low Energies and Leptogenesis
• Neutrino Mass Matrix Running for Non-Degenerate See-Saw Scales
• Neutrino Masses, Lepton Flavor Mixing and Leptogenesis in the Minimal Seesaw Model
• Radiatively induced leptogenesis in a minimal seesaw model
• Degenerate and Quasi Degenerate Majorana Neutrinos
• The CP-asymmetry in resonant leptogenesis
• Running Neutrino Masses, Leptonic Mixing Angles and CP-Violating Phases: From $M_{\mathrm{Z}}$ to ${\Lambda }_{\mathrm{GUT}}$
• Resonant enhancement in leptogenesis
• Renormalization group running of neutrino parameters
• A See-Saw Model for Atmospheric and Solar Neutrino Oscillations
• Enlarging the window for radiative leptogenesis
• Radiative Corrections to Neutrino Mixing and CP Violation in the Minimal Seesaw Model with Leptogenesis
• CP violation and Leptogenesis in models with Minimal Lepton Flavour Violation
• Degenerate minimal see-saw and leptogenesis
• Supersymmetric Jarlskog Invariants: the Neutrino Sector
• Radiative Generation of Leptonic CP Violation
• A Novel Parametrization of tau-lepton Dominance and Simplified One-loop Renormalization-group Equations of Neutrino Mixing Angles and CP-violating Phases
• CP Violation in Seesaw Model
• The $\mu -\tau$ reflection symmetry of Dirac neutrinos and its breaking effect via quantum corrections
• The number of sufficient and necessary conditions for CP conservation with Majorana neutrinos: three or four?
• Mass Bounds on Light and Heavy Neutrinos from Radiative MFV Leptogenesis
• Integral solutions to the one-loop renormalization-group equations for lepton flavor mixing parameters and the Jarlskog invariant
• Radiative leptogenesis in minimal seesaw models
• Radiative corrections to the leptonic Dirac CP-violating phase
• Impact of Fermion Mass Degeneracy on Flavor Mixing
• Leptonic unitarity triangles: RGE running effects and $\mu$-$\tau$ reflection symmetry breaking
• Naumov- and Toshev-like relations in the renormalization-group evolution of quarks and Dirac neutrinos
• Neutrino Physics and Leptonic Weak Basis Invariants

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• The number of sufficient and necessary conditions for CP conservation with Majorana neutrinos: three or four?
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• Heavy Neutral Leptons -- Advancing into the PeV domain
• Tri-Resonant Leptogenesis in a Seesaw Extension of the Standard Model
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• Spelling Out Leptonic CP Violation in the Language of Invariant Theory
• Comment on "Flavor invariants and renormalization-group equations in the leptonic sector with massive Majorana neutrinos"
• Leptonic CP violation from the seesaw
• Weak-basis invariants and CP conservation in the leptonic sector with Majorana neutrinos
• Flavour Invariants of the N Higgs Doublet Model
• Hilbert Series for Leptonic Flavor Invariants in the Minimal Seesaw Model