Lepton mixing predictions from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>6</mml:mn><mml:msup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:math> family symmetry

King, Stephen F.; Neder, Thomas; Stuart, A.

doi:10.1016/j.physletb.2013.08.052

Cited by 88 publications

(51 citation statements)

References 24 publications

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“…This group however is not so interesting according to [22], since it permits several more invariants than the groups associated with discrete minimal flavor violation in the quark sector. 6 Similar observations can also be made in the analyses found in [13][14][15].…”

Section: Introductionsupporting

confidence: 78%

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Mixing patterns from the groups Σ(nφ)

Hagedorn¹,

Meroni²,

Vitale³

2014

J. Phys. A: Math. Theor.

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We survey the mixing patterns which can be derived from the discrete groups Σ(36 × 3), Σ(72 × 3), Σ(216 × 3) and Σ(360 × 3), if these are broken to abelian subgroups G e and G ν in the charged lepton and neutrino sector, respectively. Since only Σ(360 × 3) possesses Klein subgroups, only this group allows neutrinos to be Majorana particles. We find a few patterns that can agree well with the experimental data on lepton mixing in scenarios with small corrections and that predict the reactor mixing angle θ 13 to be 0.1 θ 13 0.2. All these patterns lead to a trivial Dirac phase. Patterns which instead reveal CP violation tend to accommodate the data not well. We also comment on the outer automorphisms of the discussed groups, since they can be useful for relating inequivalent representations of these groups.

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Section: Introductionsupporting

confidence: 78%

“…12 Such type of pattern has already been found [6,11,13,14], when studying groups belonging to the series ∆(6n 2 ), n ∈ N . In [6,11] it has been suggested that there might be a general rule, namely for G e = Z 3 , G ν = Z 2n and G l = ∆(6n 2 ) the angle θ reads θ = ±π/(2n).…”

Section: Group σ(216 × 3)mentioning

confidence: 76%

Mixing patterns from the groups Σ(nφ)

Hagedorn¹,

Meroni²,

Vitale³

2014

J. Phys. A: Math. Theor.

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“…Similarly m ν respects the S, U symmetry (see Eq.62) preserved by the φ ν VEV. In such a "direct approach" the full Klein symmetry Z S 2 × Z U 2 of the neutrino mass matrix arises as a subgroup of the initial family symmetry G. Given the measurement of the reactor angle, the only viable direct models are those based on ∆(6N 2 ) [84][85][86], with quite large N required. Such models generally predict TM 2 mixing and a CP phase δ = 0, π, both of which are disfavoured by current data.…”

Section: Klein Symmetry and Direct Modelsmentioning

confidence: 99%

Unified models of neutrinos, flavour andCPViolation

King

2017

Progress in Particle and Nuclear Physics

232

164

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Recent data from neutrino experiments gives intriguing hints about the mass ordering, the CP violating phase and non-maximal atmospheric mixing. There seems to be a (one sigma) preference for a normal ordered (NO) neutrino mass pattern, with a CP phase δ = −100 • ± 50 • , and (more significantly) non-maximal atmospheric mixing. Global fits for the NO case yield lepton mixing angle one sigma ranges:Cosmology gives a limit on the total of the three masses to be below about 0.23 eV, favouring hierarchical neutrino masses over quasi-degenerate masses. Given such experimental advances, it seems an opportune moment to review the theoretical status of attempts to explain such a pattern of neutrino masses and lepton mixing, focussing on approaches based on the four pillars of: predictivity, minimality, robustness and unification. Predictivity can result from various mixing sum rules whose status is reviewed. Minimality can follow from the type I seesaw mechanism, including constrained sequential dominance of right-handed (RH) neutrinos, and the littlest seesaw model. Robustness requires enforcing a discrete CP and non-Abelian family symmetry, spontaneously broken by flavons with the symmetry preserved in a semi-direct way. Unification can account for all lepton and quark masses, mixing angles and CP phases, as in Supersymmetric Grand Unified Theories of Flavour, with possible string theory origin.

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“…The direct approach of the S 4 symmetry predicts the TBM, which is inconsistent with the vanishing θ 13 . Therefore, the larger groups of G are examined in Δ(6n 2 ) [66], such as Δ(96) [67], in the direct approach.…”

Section: Direct Approach Of S 4 Symmetrymentioning

confidence: 99%

Neutrinos and flavor symmetries

Tanimoto

2015

AIP Conference Proceedings

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Abstract. We discuss the recent progress of flavor models with the non-Abelian discrete symmetry in the lepton sector focusing on the θ 13 and CP violating phase. In both direct approach and indirect approach of the flavor symmetry, the nonvanishing θ 13 is predictable. The flavor symmetry with the generalised CP symmetry can also predicts the CP violating phase. We show the phenomenological analyses of neutrino mixing for the typical flavor models.

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Lepton mixing predictions from Δ(6n2) family symmetry

Cited by 88 publications

References 24 publications

Mixing patterns from the groups Σ(nφ)

Mixing patterns from the groups Σ(nφ)

Unified models of neutrinos, flavour andCPViolation

Neutrinos and flavor symmetries

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