Deviation from Tri-Bimaximal Mixing and Large Reactor Mixing Angle

Recent observations for a non-zero $\theta_{13}$ have come from various experiments. We study a model of lepton mixing with a 2-3 flavor symmetry to accommodate the sizable $\theta_{13}$ measurement. In this work, we derive deviations from the tri-bimaximal (TBM) pattern arising from breaking the flavor symmetry in the neutrino sector, while the charged leptons contribution has been discussed in a previous work. Contributions from both sectors towards accommodating the non-zero $\theta_{13}$ measurement are presented.Comment: 25 pages, 12 figures. arXiv admin note: text overlap with arXiv:1109.232

Tri-Bimaximal Lepton Mixing and Leptogenesis

In models with flavour symmetries added to the gauge group of the Standard Model the CP-violating asymmetry necessary for leptogenesis may be related with low-energy parameters. A particular case of interest is when the flavour symmetry produces exact Tri-Bimaximal lepton mixing leading to a vanishing CP-violating asymmetry. In this paper we present a model-independent discussion that confirms this always occurs for unflavoured leptogenesis in type I see-saw scenarios, noting however that Tri-Bimaximal mixing does not imply a vanishing asymmetry in general scenarios where there is interplay between type I and other see-saws. We also consider a specific model where the exact Tri-Bimaximal mixing is lifted by corrections that can be parametrised by a small number of degrees of freedom and analyse in detail the existing link between low and high-energy parameters - focusing on how the deviations from Tri-Bimaximal are connected to the parameters governing leptogenesis.Comment: 29 pages, 6 figures; version 2: references added, minor correction

CKM and Tri-bimaximal MNS Matrices in a SU(5) x (d)T Model

We propose a model based on SU(5) x {}^{(d)}T which successfully gives rise to near tri-bimaximal leptonic mixing as well as realistic CKM matrix elements for the quarks. The Georgi-Jarlskog relations for three generations are also obtained. Due to the {}^{(d)}T transformation property of the matter fields, the b-quark mass can be generated only when the {}^{(d)}T symmetry is broken, giving a dynamical origin for the hierarchy between m_{b} and m_{t}. There are only nine operators allowed in the Yukawa sector up to at least mass dimension seven due to an additional Z_{12} x Z'_{12} symmetry, which also forbids, up to some high orders, operators that lead to proton decay. The resulting model has a total of nine parameters in the charged fermion and neutrino sectors, and hence is very predictive. In addition to the prediction for \theta_{13} \simeq \theta_{c}/3 \sqrt{2}, the model gives rise to a sum rule, \tan^{2}\theta_{\odot} \simeq \tan^{2} \theta_{\odot, \mathrm{TBM}} - {1/2} \theta_{c} \cos\beta, which is a consequence of the Georgi-Jarlskog relations in the quark sector. This deviation could account for the difference between the experimental best fit value for the solar mixing angle and the value predicted by the tri-bimaximal mixing matrix.Comment: 11 pages; v2: additional references added; minor modifications made; conclusion unchanged; v3: version to appear in Phys. Lett.

A Maximal Atmospheric Mixing from a Maximal CP Violating Phase

We point out an elegant mechanism to predict a maximal atmospheric angle, which is based on a maximal CP violating phase difference between second and third lepton families in the flavour symmetry basis. In this framework, a discussion of the predictions for theta_{12}, |U_{e3}|, delta and their possible correlations is provided. We also present an explicit realisation in terms of an SO(3) flavour symmetry model.Comment: v2=published version: 11 pages, 4 figures, text improved, reference adde

Tri-bimaximal Neutrino Mixing from A(4) and \theta_{13} \sim \theta_C

It is a common believe that, if the Tri-bimaximal mixing (TBM) pattern is explained by vacuum alignment in an A(4) model, only a very small reactor angle, say \theta_{13} \sim \lambda^2_C being \lambda_C \equiv \theta_C the Cabibbo angle, can be accommodated. This statement is based on the assumption that all the flavon fields acquire VEVs at a very similar scale and the departures from exact TBM arise at the same perturbation level. From the experimental point of view, however, a relatively large value \theta_{13} \sim \lambda_C is not yet excluded by present data. In this paper, we propose a Seesaw A(4) model in which the previous assumption can naturally be evaded. The aim is to describe a \theta_{13} \sim \lambda_C without conflicting with the TBM prediction for \theta_{12} which is rather close to the observed value (at \lambda^2_C level). In our model the deviation of the atmospherical angle from maximal is subject to the sum-rule: \sin ^2 \theta_{23} \approx 1/2 + \sqrt{2}/2 \sin \delta \cos \theta_{13} which is a next-to-leading order prediction of our model.Comment: 16 pages, revised, typos corrected, references adde

Tri-bimaximal Neutrino Mixing and Quark Masses from a Discrete Flavour Symmetry

We build a supersymmetric model of quark and lepton masses based on the discrete flavour symmetry group T', the double covering of A_4. In the lepton sector our model is practically indistinguishable from recent models based on A_4 and, in particular, it predicts a nearly tri-bimaximal mixing, in good agreement with present data. In the quark sector a realistic pattern of masses and mixing angles is obtained by exploiting the doublet representations of T', not available in A_4. To this purpose, the flavour symmetry T' should be broken spontaneously along appropriate directions in flavour space. In this paper we fully discuss the related vacuum alignment problem, both at the leading order and by accounting for small effects coming from higher-order corrections. As a result we get the relations: \sqrt{m_d/m_s}\approx |V_{us}| and \sqrt{m_d/m_s}\approx |V_{td}/V_{ts}|.Comment: 27 pages, 1 figure; minor correction

Trimaximal neutrino mixing from vacuum alignment in A4 and S4 models

Recent T2K results indicate a sizeable reactor angle theta_13 which would rule out exact tri-bimaximal lepton mixing. We study the vacuum alignment of the Altarelli-Feruglio A4 family symmetry model including additional flavons in the 1' and 1" representations and show that it leads to trimaximal mixing in which the second column of the lepton mixing matrix consists of the column vector (1,1,1)^T/sqrt{3}, with a potentially large reactor angle. In order to limit the reactor angle and control the higher order corrections, we propose a renormalisable S4 model in which the 1' and 1" flavons of A4 are unified into a doublet of S4 which is spontaneously broken to A4 by a flavon which enters the neutrino sector at higher order. We study the vacuum alignment in the S4 model and show that it predicts accurate trimaximal mixing with approximate tri-bimaximal mixing, leading to a new mixing sum rule testable in future neutrino experiments. Both A4 and S4 models preserve form dominance and hence predict zero leptogenesis, up to renormalisation group corrections.Comment: 24 pages, 2 figures, version to be published in JHE

Obtaining the Neutrino Mixing Matrix with the Tetrahedral Group

We discuss various "minimalist'' schemes to derive the neutrino mixing matrix using the tetrahedral group $A_{4}.

Model-Independent Analysis of Tri-bimaximal Mixing -- a Softly-Broken Hidden or an Accidental Symmetry?

To address the issue of whether tri-bimaximal mixing (TBM) is a softly-broken hidden or an accidental symmetry, we adopt a model-independent analysis in which we perturb a neutrino mass matrix leading to TBM in the most general way but leave the three texture zeros of the diagonal charged lepton mass matrix unperturbed. We compare predictions for the perturbed neutrino TBM parameters with those obtained from typical SO(10) grand unified theories with a variety of flavor symmetries. Whereas SO(10) GUTs almost always predict a normal mass hierarchy for the light neutrinos, TBM has a priori no preference for neutrino masses. We find, in particular for the latter, that the value of |U_{e3}| is very sensitive to the neutrino mass scale and ordering. Observation of |U_{e3}|^2 > 0.001 to 0.01 within the next few years would be incompatible with softly-broken TBM and a normal mass hierarchy and would suggest that the apparent TBM symmetry is an accidental symmetry instead. No such conclusions can be drawn for the inverted and quasi-degenerate hierarchy spectra.Comment: 14 pages, 8 figures. Typos corrected, references added. To appear in PL

Lepton Flavour Violation in a Supersymmetric Model with A4 Flavour Symmetry

We compute the branching ratios for mu-> e gamma, tau-> mu gamma and tau -> e gamma in a supersymmetric model invariant under the flavour symmetry group A4 X Z3 X U(1)_{FN}, in which near tri-bimaximal lepton mixing is naturally predicted. At leading order in the small symmetry breaking parameter u, which is of the same order as the reactor mixing angle theta_{13}, we find that the branching ratios generically scale as u^2. Applying the current bound on the branching ratio of mu -> e gamma shows that small values of u or tan(beta) are preferred in the model for mass parameters m_{SUSY} and m_{1/2} smaller than 1000 GeV. The bound expected from the on-going MEG experiment will provide a severe constraint on the parameter space of the model either enforcing u approx 0.01 and small tan(beta) or m_{SUSY} and m_{1/2} above 1000 GeV. In the special case of universal soft supersymmetry breaking terms in the flavon sector a cancellation takes place in the amplitudes and the branching ratios scale as u^4, allowing for smaller slepton masses. The branching ratios for tau -> mu gamma and tau -> e gamma are predicted to be of the same order as the one for mu -> e gamma, which precludes the possibility of observing these tau decays in the near future.Comment: 44 page