Lepton Mixing Parameters from Discrete and CP Symmetries

Feruglio, Ferruccio; Hagedorn, Claudia; Ziegler, Robert

doi:10.48550/arxiv.1211.5560

Cited by 76 publications

(261 citation statements)

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“…The black and blue points are mixing patterns that can be produced by the flavor group ∆(96), the green and red points can be derived from ∆(384) while the group ∆(1536) generates mixing angles represented by the pink and orange points. This will be reviewed in Section 3. leptonic mixing matrix is given by U PMNS = U HPS U 13 (θ, δ) [30][31][32][33][34][35][36]. This mixing pattern leads to sin 2 θ 12 > 1/3 and is sometimes known as tri-maximal pattern TM2.…”

Section: Leptonic Mixing From Remnant Symmetriesmentioning

confidence: 99%

Lepton mixing patterns from a scan of finite discrete groups

2013

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The recent discovery of a non-zero value of the mixing angle θ 13 has ruled out tribimaximal mixing as the correct lepton mixing pattern generated by some discrete flavor symmetry (barring large next-to-leading order corrections in concrete models). In this work we assume that neutrinos are Majorana particles and perform a general scan of all finite discrete groups with order less than 1536 to obtain their predictions for lepton mixing angles. To our surprise, the scan of over one million groups only yields 3 interesting groups that give lepton mixing patterns which lie within 3-sigma of the current best global fit values. A systematic way to categorize such groups and the implications for flavor symmetry are discussed.

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Section: Leptonic Mixing From Remnant Symmetriesmentioning

confidence: 99%

Lepton mixing patterns from a scan of finite discrete groups

2013

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“…The realization of zero textures by discrete symmetry or continuous symmetry has been discussed in several studies [61,63,65]. Meanwhile, µ − τ reflection symmetry naturally appear from GCP and S 4 symmetry [8,13,66]. Because diagonal reflection symmetries are equivalent to two different µ − τ symmetries, a similar model building would be possible.…”

Section: Representation Of Ckm Matrix Texture and Symmetriesmentioning

confidence: 99%

Almost exact diagonal reflection symmetries and three-zero texture

Yang

2021

Preprint

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In this paper, we consider the diagonal reflection symmetries and three-zero texture in the SM. The three-zero texture has two less assumptions ((Mu)11, (Mν)11 = 0) than the universal four-zero texture for mass matrices (M f )11 = (M f )13,31 = 0 for f = u, d, ν, e. The texture and symmetries reproduce the CKM and MNS matrices with accuracies of O(10 −4 ) and O(10 −3 ).By assuming a de unified relation (M d ∼ Me), this system predicts the normal hierarchy, the Dirac phase δCP ≃ 202 • , the Majorana phases α12 = 11.3 • , α13 = 6.90 • up to π, and the lightest neutrino mass m1 ≃ 2.97 − 4.72 [meV]. The effective mass of the double beta decay |mee| is found to be 1.24 ∼ 1.77 [meV].

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“…Therefore, our constraint on the VEVs is independent of the precise form of the potential and simply reveals what (orbits of) VEVs are possible in principle. 16 In order to check which of the non-trivial solutions to (7.8) really is a stationary point of the potential and to fix remaining free parameters, one still has to plug an element of Φ into the gradient of the potential.…”

Section: A Necessary Condition On the Vevsmentioning

confidence: 99%

“…Thus, understanding outer automorphisms is essential to understand CP. For instance, understanding the interrelation of CP and discrete Groups [5,16] has enabled the discovery that settings based on certain discrete groups preclude CP symmetries altogether [17]. Despite their relevance to Nature, however, outer automorphisms have generally not received a lot of attention in the literature.…”

Section: Introductionmentioning

confidence: 99%

Symmetries of symmetries and geometrical CP violation

Fallbacher

Trautner

2015

Nuclear Physics B

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We investigate transformations which are not symmetries of a theory but nevertheless leave invariant the set of all symmetry elements and representations. Generalizing from the example of a three Higgs doublet model with $\Delta(27)$ symmetry, we show that the possibility of such transformations signals physical degeneracies in the parameter space of a theory. We show that stationary points only appear in multiplets which are representations of the group of these so-called equivalence transformations. As a consequence, the stationary points are amongst the solutions of a set of homogeneous linear equations. This is relevant to the minimization of potentials in general and sheds new light on the origin of calculable phases and geometrical CP violation.Comment: 20+9 pages, 1 figure; v1: minor changes, added clarification, matches the published versio

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Lepton Mixing Parameters from Discrete and CP Symmetries

Cited by 76 publications

References 0 publications

Lepton mixing patterns from a scan of finite discrete groups

Lepton mixing patterns from a scan of finite discrete groups

Almost exact diagonal reflection symmetries and three-zero texture

Symmetries of symmetries and geometrical CP violation

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