CP and discrete flavour symmetries

We propose a complex extension of µτ permutation antisymmetry in the neutrino Majorana matrix M ν . The latter can be realized for the Lagrangian by appropriate CP transformations on the neutrino fields. The resultant form of M ν is shown to be simply related to that with a complex (CP) extension of µτ permutation symmetry, with identical phenomenological consequences, though their group theoretic origins are quite different. We investigate those consequences in detail for the minimal seesaw induced by two strongly hierarchical right-chiral neutrinos N 1 and N 2 with the result that the Dirac phase is maximal while the two Majorana phases are either 0 or π. We further provide an uptodate discussion of the ββ0ν process vis-a-vis ongoing and forthcoming experiments. Finally, a thorough treatment is given of baryogenesis via leptogenesis in this scenario, primarily with the assumption that the lepton asymmetry produced by the decays of N 1 only matters here with the asymmetry produced by N 2 being washed out. Tight upper and lower bounds on the mass of N 1 are obtained from the constraint of obtaining the correct observed range of the baryon asymmetry parameter and the role played by N 2 is elucidated thereafter. The mildly hierarchical right-chiral neutrino case (including the quasidegenerate possibility) is discussed in an appendix.

Section: Complex Extension Of µτ Antisymmetrymentioning

confidence: 99%

Consequences of minimal seesaw with complex μτ antisymmetry of neutrinos

Samanta

Roy

Ghosal

2018

“…Then the two symmetries act on the same space and CP µτ induces the following automorphism on Z 8 [50][51][52][53]:…”

Section: Jhep01(2017)068mentioning

confidence: 99%

“…[39] for a review. In contrast, residual CP symmetries have also been considered to determine the mixing angles (and CP phases) [40][41][42][43][50][51][52][53].…”

Section: Introductionmentioning

confidence: 99%

“…The combination of two noncommuting symmetries cannot be arbitrary and needs to fulfill some compatibility rules so that the whole group closes. 3 In fact, some consistency conditions are required to combine a CP symmetry with a nonabelian discrete flavor group [50][51][52][53]. For this reason, we choose the simplest setting where we combine an abelian discrete symmetry with CP µτ in a consistent but nontrivial way.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Mu-tau reflection symmetry with a texture-zero

Nishi

Sánchez-Vega

2017

Abstract:The µτ -reflection symmetry is a simple symmetry capable of predicting all the unknown CP phases of the lepton sector and the atmospheric angle but too simple to predict the absolute neutrino mass scale or the mass ordering. We show that by combining it with a discrete abelian symmetry in a nontrivial way we can additionally enforce a texture-zero and obtain a highly predictive scenario where the lightest neutrino mass is fixed to be in the few meV range for two normal ordering (NO) solutions or in the tens of meV in one inverted ordering (IO) solution. The rate for neutrinoless double beta decay is predicted to be negligible for NO or have effective mass m ββ ≈ 14-29 meV for IO, right in the region to be probed in future experiments.

“…The basic idea is to impose CP conservation on the theory so that all couplings and masses are real. Note that the A 4 assignments in table 1 do not involve the complex singlets 1 , 1 or any complex Clebsch-Gordan coefficients so that the definition of CP is straightforward in this model and hence all the different ways that CP may be defined in A 4 [44][45][46][47][48] are equivalent for our purposes (see [42,43] for a discussion of this point). The CP symmetry is broken in a discrete way by the form of the superpotential terms.…”

Section: Jhep01(2014)119mentioning

confidence: 99%

A model of quark and lepton mixing

King

2014

We propose a model of quark and lepton mixing based on the tetrahedral A 4 family symmetry with quark-lepton unification via the tetra-colour Pati-Salam gauge group SU(4) P S , together with SU(2) L × U(1) R . The "tetra-model" solves many of the flavour puzzles and remarkably gives ten predictions at leading order, including all six PMNS parameters. The Cabibbo angle is approximately given by θ C ≈ 1/4, due to the tetravacuum alignment (1, 4, 2), providing the Cabibbo connection between quark and lepton mixing. Higher order corrections are responsible for the smaller quark mixing angles and CP violation and provide corrections to the Cabibbo and lepton mixing angles and phases. The tetra-model involves an SO(10)-like pattern of Dirac and heavy right-handed neutrino masses, with the strong up-type quark mass hierarchy cancelling in the see-saw mechanism, leading to a normal hierarchy of neutrino masses with an atmospheric angle in the first octant, θ l 23 = 40 • ± 1 • , a solar angle θ l 12 = 34 • ± 1 • , a reactor angle θ l 13 = 9.0 • ± 0.5 • , depending on the ratio of neutrino masses m 2 /m 3 , and a Dirac CP violating oscillation phase δ l = 260 • ± 5 • .