A review of μ - τ flavor symmetry in neutrino physics

In light of the latest neutrino oscillation data, we examine whether the leptonic flavor mixing matrix can take on an exact form of tri-bimaximal (TBM), golden-ratio (GR) or bimaximal (BM) mixing pattern at a superhigh-energy scale, where such a mixing pattern could be realized by a flavor symmetry, and become compatible with experimental data at the low-energy scale. Within the framework of the Minimal Supersymmetric Standard Model (MSSM), the only hope for realizing such a possibility is to count on the corrections from the renomalization-group (RG) running. In this work we focus on these radiative corrections, and fully explore the allowed parameter space for each of these mixing patterns. We find that when the upper bound on the sum of neutrino masses Σ ν ≡ m 1 + m 2 + m 3 < 0.23 eV at the 95% confidence level from Planck 2015 is taken into account, none of these mixing patterns can be identified as the leptonic mixing matrix below the seesaw threshold. If this cosmological upper bound on the sum of neutrino masses were relaxed, the TBM and GR mixing patterns would still be compatible with the latest neutrino oscillation data at the 3σ level, but not at the 1σ level. Even in this case, no such a possibility exists for the BM mixing.

Section: Jhep09(2016)167supporting

confidence: 64%

Viability of exact tri-bimaximal, golden-ratio and bimaximal mixing patterns and renormalization-group running effects

Zhang

Zhou

2016

“…This form for the neutrino mass matrix in the flavor basis (diagonal charged lepton masses) is known to predict maximal θ 23 = 45 • and δ = ±90 • at the same time that θ 13 = 0 is allowed [4][5][6]. Additionally, the Majorana phases are trivial and four discrete choices for the CP parities are possible [4][5][6]9].…”

Section: Jhep01(2017)068mentioning

confidence: 96%

“…One of the simplest symmetries that can predict all the CP phases and yet allow CP violation is the symmetry known as µτ -reflection symmetry or CP µτ symmetry where the neutrino sector is invariant by exchange of the muon neutrino with the tau antineutrino [4][5][6]. This symmetry ensures that the Dirac CP phase is maximal (δ = ±90 • ) while the Majorana phases are trivial allowing the possibility of discrete choices of the CP parities.…”

Section: Introductionmentioning

confidence: 99%

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.

“…Further, the formulation of a viable scheme of baryogenesis via leptogenesis within this scenario is a challenging task. There has also been a substantial amount of work with discrete flavor symmetries of the light neutrino Majorana mass matrix: specifically real µτ permutation symmetry [22][23][24][25][26][27][28][29][30][31] and its complex (CP) extension [32][33][34] as well as real µτ permutation antisymmetry [35] but not the complex (CP) extension of that. This last mentioned topic will be the subject of our attention in this paper with the aim of predicting the neutrino CP phases.…”

Section: Introductionmentioning

confidence: 99%

Consequences of minimal seesaw with complex μτ antisymmetry of neutrinos

Samanta

Roy

Ghosal

2018

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.