What does<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>μ</mml:mi><mml:mo>−</mml:mo><mml:mi>τ</mml:mi></mml:math>symmetry imply about neutrino mixings?

Fuki, Kenichi; Yasuè, Masaki

doi:10.1103/physrevd.73.055014

Cited by 40 publications

(26 citation statements)

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“…* ) If the µ-τ symmetry breaking is included, there are two categories of textures respectively referred to as (C1) and (C2). 18) In the category (C1), we have sin 2θ 23 ≈ σ (σ = ±1) and sin 2 θ 13 ≪ 1 while in the category (C2), we have sin 2θ 23 ≈ −σ and ∆m 2 ⊙ /|∆m 2 atm | ≪ 1. In the category (C2), the µ-τ symmetric limit is signaled by sin θ 12 → 0 instead of sin θ 13 → 0.…”

Section: §1 Introductionmentioning

confidence: 88%

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Majorana CP Violation in Approximately - Symmetric Models with det(M ) = 0

Baba¹,

Yasuè²

2010

Progress of Theoretical Physics

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We discuss effects of Majorana CP violation in a model-independent way for a given phase structure of flavor neutrino masses. To be more predictive, we confine ourselves to models with det(M ν ) = 0, where M ν is a flavor neutrino mass matrix, and to be consistent with observed results of the neutrino oscillation, the models are subject to an approximate μ-τ symmetry. There are two categories of approximately μ-τ symmetric models classified as (C1) yielding sin 2 2θ 23 ≈ 1 and sin 2 θ 13 1 and (C2) yielding sin 2 2θ 23 ≈ 1 and Δm 2 /|Δm 2 atm | 1, where θ 23(13) stands for the mixing of massive neutrinos ν 2 and ν 3 (ν 1 and ν 3 ) and Δm 2 (Δm 2 atm ) stands for the mass squared difference for atmospheric (solar) neutrinos. The Majorana phase can be large for the normal mass hierarchy and for the inverted mass hierarchy with m 1 ≈ −m 2 only realized in (C1) while they are generically small for the inverted mass hierarchy with m 1 ≈ m 2 in both (C1) and (C2). These results do not depend on a specific choice of phases in M ν but hold true in any models with det(M ν ) = 0 because of the rephasing invariance.Subject Index: 152, 154 §1. IntroductionNeutrinos are oscillating and mixed with each other among three flavor neutrinos. Such oscillations have been confirmed to occur for the atmospheric neutrinos, 1) the solar neutrinos, 2), 3) the reactor neutrinos 4) and the accelerator neutrinos. 5) Three massive neutrinos have masses m 1,2,3 measured as mass squared differences defined by Δm 2 = m 2 2 −m 2 1 and Δm 2 atm = m 2 3 −m 2 1 . Three flavor neutrinos ν e,μ,τ are mixed into three massive neutrinos ν 1,2,3 during their flight and the mixing can be described by the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrix 6) parameterized by three mixing angles θ 12,23,13 , one Dirac CP violating phase δ CP and three Majorana phase φ 1,2,3 , 7) where Majorana CP violating phases are given by two combinations of φ 1,2,3 .It is CP property of neutrinos that has currently received much attention since the similar CP property of quarks has been observed and successfully described by the Kobayashi-Maskawa mixing matrix. 8) If neutrinos exhibit CP violation, there is a new seed to produce the baryon number in the Universe by the Fukugida-Yanagida mechanism of the leptogenesis, 9) which favors the seesaw mechanism 10) of creating tiny neutrino masses. However, there is no direct linkage between CP violation of three flavor neutrinos and that of the leptogenesis since the CP violating phases are associated with heavy neutrinos but not with three flavor neutrinos. If the number * )

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Section: §1 Introductionmentioning

confidence: 88%

“…4). As a plausible choice, we obtain 18) sin θ 13 = 0, sin θ 23 = σ √ 2 , δ = γ = 0, (2 . 5) as a category (C1) or sin θ 12 = 0, sin…”

Section: §1 Introductionmentioning

confidence: 99%

Majorana CP Violation in Approximately - Symmetric Models with det(M ) = 0

Baba¹,

Yasuè²

2010

Progress of Theoretical Physics

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“…Another notable feature of TBM is that it exhibits µ-τ symmetry. [56] This can be easily demonstrated by examining the first and second columns of U 2 TBM and noting that they are identical. Physically this implies that ν µ and ν τ have identical superpositions of the three neutrino mass eigenstates.…”

Section: µ-τ Symmetrymentioning

confidence: 97%

Dark matter from binary tetrahedral flavor symmetry

Eby

Frampton

2012

Physics Letters B

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DAVID A. EBY: Binary Tetrahedral Flavor Symmetry. (Under the direction of Paul H. Frampton)A study of the T ′ Model and its variants utilizing Binary Tetrahedral Flavor Symmetry. We begin with a description of the historical context and motivations for this theory, together with some conceptual background for added clarity, and an account of our theory's inception in previous works. Our model endeavors to bridge two categories of particles, leptons and quarks, a unification made possible by the inclusion of additional Higgs particles, shared between the two fermion sectors and creating a single coherent system. This is achieved through the use of the Binary Tetrahedral symmetry group and an investigation of the Tribimaximal symmetry evidenced by neutrinos. Our work details perturbations and extensions of this T ′ Model as we apply our framework to neutrino mixing, quark mixing, unification, and dark matter. Where possible, we evaluate model predictions against experimental results and find excellent matching with the atmospheric and reactor neutrino mixing angles, an accurate prediction of the Cabibbo angle, and a dark matter candidate that remains outside the limits of current tests. Additionally, we include mention of a number of unanswered questions and remaining areas of interest for future study. Taken together, we believe these results speak to the promising potential of finite groups and flavor symmetries to act as an approximation of nature.iii First and foremost, David Eby is grateful to Paul Frampton, his longtime advisor, co-author, and colleague for his guidance and his irreplaceable assistance in completing his research and this dissertation. David is also grateful to the rest of his committee, Y. Jack Ng in particular, for their backing despite trying circumstances.He would like to thank his friends for their support and the department for its counsel and instruction. He would also like to express his gratitude to Shinya Matsuzaki, the former group postdoc, for useful discussions and a productive collaboration. He wishes to thank his Family for their enduring love and, lastly, sends thanks to those unmentioned that have aided in his work and his life.iv List of AbbreviationsA 4 Tetrahedral Symmetry Group BSM Beyond the Standard Model CKM Cabbibo-Kobayashi-Maskawa matrix CP Charge-Parity Symmetry IH Inverted Neutrino Mass Hierarchy irrep Irreducible Representation MRT ′ M Minimal Renormalizable T ′ Model MSM Minimal Standard Model NH Normal Neutrino Mass Hierarchy NMRT ′ M Next-to-Minimal Renormalizable T ′ Model PMNS Pontecorvo-Maki-Nakagawa-Sakata matrix QCD Quantum Chromodynamics QED Quantum Electrodynamics SUSY Supersymmetry T ′ Binary Tetrahedral Symmetry Group TBM Tribimaximal Mixing VEV Vacuum Expectation Value

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“…Aizawa and Yasue [7] analysis complex neutrino mass texture and the µ − τ symmetry which can yield small θ 13 as a µ − τ breaking effect. The µ − τ symmetry breaking effect in relation with the small θ 13 also discussed in [8]. Analysis of the correlation between CP violation and the µ − τ symmetry breaking can be read in [9,10,11,12].…”

Section: Broken µ − τ Symmetrymentioning

confidence: 99%

NONZERO θ₁₃ AND CP VIOLATION FROM BROKEN μ – τ SYMMETRY WITH m₁ = 0

Damanik

2015

Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects

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Nonzero and relatively large of θ 13 mixing angle has some phenomenological consequences on neutrino physics beyond the standard model. One of the consequences if the mixing angle θ 13 = 0 is the possibility of the CP violation on the neutrino sector. In order to obtain nonzero θ 13 mixing angle, we break the neutrino mass matrix that obey µ− τ symmetry by introducing a complex parameter and determine the Jarlskog invariant as a measure of CP violation existence. By using the experimental data as input, we determine the Dirac phase δ as function of mixing angle θ 13 .

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What doesμ−τsymmetry imply about neutrino mixings?

Cited by 40 publications

References 76 publications

Majorana CP Violation in Approximately - Symmetric Models with det(M ) = 0

Majorana CP Violation in Approximately - Symmetric Models with det(M ) = 0

Dark matter from binary tetrahedral flavor symmetry

NONZERO θ₁₃ AND CP VIOLATION FROM BROKEN μ – τ SYMMETRY WITH m₁ = 0

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What doesμ−τsymmetry imply about neutrino mixings?

Cited by 40 publications

References 76 publications

Majorana CP Violation in Approximately - Symmetric Models with det(M ) = 0

Majorana CP Violation in Approximately - Symmetric Models with det(M ) = 0

Dark matter from binary tetrahedral flavor symmetry

NONZERO θ13 AND CP VIOLATION FROM BROKEN μ – τ SYMMETRY WITH m1 = 0

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NONZERO θ₁₃ AND CP VIOLATION FROM BROKEN μ – τ SYMMETRY WITH m₁ = 0