Correlation between leptonic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math>violation and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>μ</mml:mi><mml:mtext mathvariant="normal">−</mml:mtext><mml:mi>τ</mml:mi></mml:math>symmetry breaking

Baba, Teppei; Yasuè, Masaki

doi:10.1103/physrevd.75.055001

Cited by 31 publications

(18 citation statements)

References 90 publications

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“…However, we have confirmed that the phase of the ν 2 -ν 3 mixing should be γ in place of χ to consistently describe the neutrino mixings. 14) Namely, Eq. (1 .…”

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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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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“…However, we have confirmed that the phase of the ν 2 -ν 3 mixing should be γ in place of χ to consistently describe the neutrino mixings. 14) Namely, Eq. (1 .…”

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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“…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]. Now, we are in position to study the effect of neutrino mass matrix that obey the µ − τ symmetry breaking in relation to the nonzero θ 13 and Jarlskog rephasing invariant J CP by breaking the neutrino mass matrix in Eq.…”

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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“…( 19), e.g., rephasing invariant expressions for Majorana phases α 2,3 , it is useful to employ general parameterization of U instead of Eq. ( 3), which is containing three Dirac phases δ, ρ and τ as well as one additional phase γ [22,27]:…”

Section: Cp-violating Phasesmentioning

confidence: 99%

CP violation in bipair neutrino mixing

Kitabayashi

Yasuè

2013

Physics Letters B

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There are experimentally determined two best-fit points for the atmospheric neutrino mixing angle θ 23 : sin 2 θ 23 = 0.413 (case A) and sin 2 θ 23 = 0.594 (case B). In the bipair neutrino mixing scheme, we predict sin 2 θ 23 = √ 2 − 1 (case 1) to be consistent with the case A and sin 2 θ 23 = 2 − √ 2 (case 2) to be consistent with the case B. If the case B is realized in nature, the bipair neutrino mixing provides a unique neutrino model consistent with the observation sin 2 θ 23 = 0.594. However, the reactor neutrino mixing angle θ 13 is predicted to be sin 2 θ 13 = 0, which is inconsistent with the observation. We propose a new modification scheme to yield sin 2 θ 13 = 0 utilizing the charged lepton contribution and study its effect on both of CPviolating Dirac and Majorana phases, which is numerically estimated. It is found that there appear striking differences between the case 1 and the case 2 in their phase structure.

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Correlation between leptonicCPviolation andμ−τsymmetry breaking

Cited by 31 publications

References 90 publications

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

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

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

CP violation in bipair neutrino mixing

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Correlation between leptonicCPviolation andμ−τsymmetry breaking

Cited by 31 publications

References 90 publications

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

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

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

CP violation in bipair neutrino mixing

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