Common origin of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>θ</mml:mi><mml:mn>13</mml:mn></mml:msub></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Δ</mml:mi><mml:msubsup><mml:mi>m</mml:mi><mml:mn>12</mml:mn><mml:mn>2</mml:mn></mml:msubsup></mml:math>in a model of neutrino mass with quaternion symmetry

To generate the minimal neutrino Majorana mass matrix that has a free solar mixing angle and ∆m 2 sol = 0 it suffices to implement an O(2) symmetry, or one of its subgroups SO(2), Z N ≥3 , or D N ≥3 . This O(2) generalizes the hidden Z s 2 of lepton mixing and leads in addition automatically to µ-τ symmetry. Flavor-democratic perturbations, as expected e.g. from the Planck scale, then result in tri-bimaximal mixing. We present a minimal model with three Higgs doublets implementing a type-I seesaw mechanism with a spontaneous breakdown of the symmetry, leading to large θ13 and small ∆m 2 sol due to the particular decomposition of the perturbations under µ-τ symmetry.

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“…A connection between the two small parameters is also discussed in Ref [12]. in a model based on the discrete quaternion group Q 8 .…”

mentioning

confidence: 94%

“Hidden” O(2) and SO(2) symmetry in lepton mixing

Heeck

Rodejohann

2012

J. High Energ. Phys.

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“…for the best fit value of θ 13 This relation follows from the fact that there are two large mixing connecting neighboring generations, and from the following two assumptions: (i) NH, (ii) absence of fine tuning between different elements of the mass matrix (e.g., m eµ = m eτ ). There are also models where the relation ( 9) is a consequence of certain symmetry [46]. A kind of Fritzsch ansatz can be used for the lepton Dirac mass matrices.…”

Section: From Special To Normal?mentioning

confidence: 99%

Neutrino 2012: Outlook – theory

Smirnov

2013

Nuclear Physics B - Proceedings Supplements

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Ongoing developments in theory and phenomenology are related to the measured large value of 1-3 mixing and indications of significant deviation of the 2-3 mixing from maximal one. "Race" for the mass hierarchy has started and there is good chance that multi-megaton scale atmospheric neutrino detectors with low threshold (e.g. PINGU) will establish the type of hierarchy. Two IceCube candidates of the PeV cosmic neutrinos if confirmed, is the beginning of new era of high energy neutrino astronomy. Accumulation of data on solar neutrinos (energy spectrum, D-N asymmetry, value of ∆m 2 21 ) may uncover some new physics. The Tri-bimaximal mixing is disfavored and the existing discrete symmetry paradigm may change. The confirmed QLC prediction, θ 13 ≈ θ C / √ 2, testifies for GUT, seesaw and some symmetry at very high scales. However, the same value of 1-3 mixing can be obtained in various ways which have different implications. The situation in lepton sector changes from special (with specific neutrino symmetries, etc.) to normal, closer to that in the quark sector. Sterile neutrinos are challenge for neutrino physics but also opportunity with many interesting phenomenological consequences. Further studies of possible connections between neutrinos and the dark sector of the Universe may lead to breakthrough both in particle physics and cosmology.

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“…The quaternion group Q, sometimes also called Q 4 or Q 8 , has 8 elements and five irreducible representations (irreps): 1 þþ , 1 þÀ , 1 Àþ , 1 ÀÀ , and 2 (following notation in [28,29]) where the two-dimensional irrep is complex.…”

Section: Appendix A: Useful Facts About Qmentioning

confidence: 99%

Model of flavor with quaternion symmetry

et al. 2011

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We present a renormalizable fermion mass model based on the symmetry $Q_4$ that accommodates all fermion masses and mixing angles in both the quark and lepton sectors. It requires the presence of only four SU(2) doublet scalar fields transforming non trivially under the flavor symmetry and the assumption of an alignment between first and second generation Yukawa couplings. No right-handed neutrinos are present in the model and neutrino masses are generated radiatively through the introduction of two additional SU(2) singlet fields charged under both hypercharge and lepton number.Comment: 24 pages, 4 figures. Title changed to meet journal requirements. References added. Version to appear in Physical Review

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Common origin ofθ13andΔm122in a model of neutrino mass with quaternion symmetry

Cited by 18 publications

References 27 publications

“Hidden” O(2) and SO(2) symmetry in lepton mixing

“Hidden” O(2) and SO(2) symmetry in lepton mixing

Neutrino 2012: Outlook – theory

Model of flavor with quaternion symmetry

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