Nearly tri-bimaximal neutrino mixing and CP violation

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: Introductionmentioning

confidence: 91%

“…4 Such an increase would be welcomed by GR, while a severe tension with the low-energy data would be generated for TBM and BM.…”

Section: Jhep09(2016)167mentioning

confidence: 99%

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

Zhang

Zhou

2016

“…This forces to study models based on the breaking of the flavour symmetry and a promising choice is the kind of realizations based on non-Abelian discrete groups which reproduce the lepton mixing matrix of the so-called tribimaximal (TB) pattern [21][22][23][24][25][26][27] (sin 2 θ TB 12 = 1/3, sin 2 θ TB 23 = 1/2 and sin θ TB 13 = 0) at leading order. This mixing scheme represents a very good approximation of the experimental measurements: the TB values for the atmospheric and the reactor angles are inside the 1σ error level, while that one for the solar angle is very close to the upper 1σ value.…”

Section: Jhep08(2010)001mentioning

confidence: 99%

The interplay between GUT and flavour symmetries in a Pati-Salam × S4 model

Toorop

Bazzocchi

Merlo

2010

Both Grand Unified symmetries and discrete flavour symmetries are appealing ways to describe apparent structures in the gauge and flavour sectors of the Standard Model. Both symmetries put constraints on the high energy behaviour of the theory. This can give rise to unexpected interplay when building models that possess both symmetries. We investigate on the possibility to combine a Pati-Salam model with the discrete flavour symmetry S 4 that gives rise to quark-lepton complementarity. Under appropriate assumptions at the GUT scale, the model reproduces fermion masses and mixings both in the quark and in the lepton sectors. We show that in particular the Higgs sector and the running Yukawa couplings are strongly affected by the combined constraints of the Grand Unified and family symmetries. This in turn reduces the phenomenologically viable parameter space, with high energy mass scales confined to a small region and some parameters in the neutrino sector slightly unnatural. In the allowed regions, we can reproduce the quark masses and the CKM matrix. In the lepton sector, we reproduce the charged lepton masses, including bottom-tau unification and the Georgi-Jarlskog relation as well as the two known angles of the PMNS matrix. The neutrino mass spectrum can present a normal or an inverse hierarchy, and only allowing the neutrino parameters to spread into a range of values between λ −2 and λ 2 , with λ ≃ 0.2. Finally, our model suggests that the reactor mixing angle is close to its current experimental bound.

“…The other groups were also examined to give the TBM [44]- [55]. The deviations from the TBM were estimated in many works [12,56]- [74]. The observation of the non-vanishing θ 13 enables the detail studies of flavor models in the context of the sum rules of mixing angles [43,75]- [83].…”

Section: Jhep12(2015)132mentioning

confidence: 99%

Testing the minimal S 4 model of neutrinos with the Dirac and Majorana phases

Shimizu

Tanimoto

2015

We propose two new simple lepton flavor models in the framework of the S 4 flavor symmetry. The neutrino mass matrices, which are given by two complex parameters, lead to the inverted mass hierarchy. The charged lepton mass matrix has the 1-2 lepton flavor mixing, which gives the non-vanishing reactor angle θ 13 . These models predict the Dirac phase and the Majorana phases, which are testable in the future experiments. The predicted magnitudes of the effective neutrino mass for the neutrino-less double beta decay are in the regions as 32 meV |m ee | 49 meV and 34 meV |m ee | 59 meV, respectively. These values are close to the expected reaches of the coming experiments. The total sum of the neutrino masses are predicted in both models as 0.0952 eV m i 0.101 eV and 0.150 eV m i 0.160 eV, respectively.