On the Quasi-fixed Point in the Running of CP-violating Phases of Majorana Neutrinos

Abstract

Taking the standard parametrization of three-flavor neutrino mixing, we carefully examine the evolution of three CP-violating phases $(\delta ,{\alpha }_1^{},{\alpha }_2^{})$ with energy scales in the realistic limit ${\theta }_{13}^{}\to 0$. If $m_3^{}$ vanishes, we find that the one-loop renormalization-group equation (RGE) of $\delta$ does not diverge and its running has no quasi-fixed point. When $m_3^{}\ne 0$ holds, we show that the continuity condition derived by Antusch {\it et al} is always valid, no matter whether the $\tau$-dominance approximation is taken or not. The RGE running of $\delta$ undergoes a quasi-fixed point determined by a nontrivial input of ${\alpha }_2^{}$ in the limit $m_1^{}\to 0$. If three neutrino masses are nearly degenerate, it is also possible to arrive at a quasi-fixed point in the RGE evolution of $\delta$ from the electroweak scale to the seesaw scale or vice versa. Furthermore, the continuity condition and the quasi-fixed point of CP-violating phases in another useful parametrization are briefly discussed.

arXiv commentRevTex 13 pages. Slight modifications made for the text, Table I and references. Results and conclusions unchanged. Accepted for publication in Phys. Lett. B

References in corpus (37)

• Big Bang Nucleosynthesis (in "The Review of Particle Properties" 2004)
• Direct Evidence for Neutrino Flavor Transformation from Neutral-Current Interactions in the Sudbury Neutrino Observatory
• First Results from KamLAND: Evidence for Reactor Anti-Neutrino Disappearance
• Tri-Bimaximal Mixing and the Neutrino Oscillation Data
• Indications of Neutrino Oscillation in a 250 km Long-baseline Experiment
• Initial Results from the CHOOZ Long Baseline Reactor Neutrino Oscillation Experiment
• Symmetries and Generalisations of Tri-Bimaximal Neutrino Mixing
• Tri-Bimaximal Neutrino Mixing from Discrete Symmetry in Extra Dimensions
• Nearly Tri-Bimaximal Neutrino Mixing and CP Violation
• Mass and Flavor Mixing Schemes of Quarks and Leptons
• Cosmological Sign of Neutrino CP Violation
• Running Neutrino Masses, Mixings and CP Phases: Analytical Results and Phenomenological Consequences
• Running Neutrino Mass Parameters in See-Saw Scenarios
• Some Simple Mixing and Mass Matrices for Neutrinos
• A_4 Symmetry and Neutrinos with Very Different Masses
• Search for Neutrino Oscillations at the Palo Verde Nuclear Reactors
• Lepton Mass Hierarchy and Neutrino Oscillations
• General RG Equations for Physical Neutrino Parameters and their Phenomenological Implications
• Large Leptonic Flavor Mixing and the Mass Spectrum of Leptons
• Atmospheric Neutrino Oscillation and a Phenomenological Lepton Mass Matrix
• Obtaining the Neutrino Mixing Matrix with the Tetrahedral Group
• Quantum corrections to neutrino masses and mixing angles
• Flavor Mixing and CP Violation of Massive Neutrinos
• Flavor Symmetries and the Description of Flavor Mixing
• Implications of neutrino data circa 2005
• Maximal Neutrino Mixing and Maximal CP Violation
• Nearly degenerate neutrinos, Supersymmetry and radiative corrections
• On the Parametrization of Flavor Mixing in the Standard Model
• Running Neutrino Masses, Leptonic Mixing Angles and CP-Violating Phases: From $M_{\mathrm{Z}}$ to ${\Lambda }_{\mathrm{GUT}}$
• Generalized Tri-bimaximal Neutrino Mixing and Its Sensitivity to Radiative Corrections
• Radiative Corrections to Neutrino Mixing and CP Violation in the Minimal Seesaw Model with Leptogenesis
• Calculable CP-violating Phases in the Minimal Seesaw Model of Leptogenesis and Neutrino Mixing
• Softly broken lepton number L_e - L_μ- L_τwith non-maximal solar neutrino mixing
• The Majorana Neutrino Mass Matrix with One Texture Zero and One Vanishing Eigenvalue
• Democratic Neutrino Mixing Reexamined
• A Novel Parametrization of tau-lepton Dominance and Simplified One-loop Renormalization-group Equations of Neutrino Mixing Angles and CP-violating Phases
• Neutrino Masses and Mixings with Flavor Symmetries

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