Current data indicates that lepton mixing is very close to the tri-bimaximal mixing scenario. In general, however, one expects deviations from any mixing scenario. We discuss several examples to perturb tri-bimaximal mixing, namely soft breaking, renormalization group running and charged lepton corrections. We also present a convenient parametrization of the PMNS matrix which takes advantage of the apparently close to tri-bimaximal mixing pattern. Finally, it is discussed how to generate values of U_{e3} which correspond to the recently found hint for non-zero U_{e3}.
We study deviations from tri-bimaximality (TBM) and quark-lepton complementarity (QLC) in a model independent way. The current neutrino experimental data is well approximated by tri-bimaximal generation mixing but the QLC relations are not satisfied with each data of 1$σ$ level. This means that there exist deviations from the complementarity. The same fact for the TBM might be checked in the future neutrino experiments. We discuss such deviations from the TBM and QLC, simultaneously. A new ratio between the deviations is introduced, and some interesting points are presented. We also show predi…
We analyze in detail the predictions of "trimaximal" neutrino mixing, which is defined by a mixing matrix with identical second column elements. This column is therefore identical to the second column in the case of tri-bimaximal mixing. We also generalize trimaximal mixing by assuming that the other rows and columns of the mixing matrix individually have the same forms as for tri-bimaximal mixing. The phenomenology of these new mixing scenarios is studied. We emphasize how trimaximal mixings can be distinguished experimentally from broken tri-bimaximal mixing.
Recent observations for a non-zero $θ_{13}$ have come from various experiments. We study a model of lepton mixing with a 2-3 flavor symmetry to accommodate the sizable $θ_{13}$ 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 $θ_{13}$ measurement are presented.
We propose a scheme, based on Δ(27) flavor symmetry and supplemented by other discrete symmetries and inverse seesaw mechanism, where both the light neutrino masses and the deviation from tri-bimaximal mixing matrix can be linked to the source of lepton number violation. The hierarchies of the charged leptons are explained. We find that the quark masses including their hierarchies and the mixing can also be constructed in a similar way.
In this paper we study a parametrized description of neutrino mixing from a phenomenological point of view. We concentrate on the parametrization in terms of higher order corrections to the leading order mixing matrix. A method to describe subleading contributions and its applications to tri-bimaximal mixing are discussed. We show that mixing matrices similar to tri-bimaximal-Cabibbo mixing can be obtained by straightforward choices of parameters. To achieve better agreement with the experimental data without increasing the number of free parameters, we impose a simple phenomenological relatio…
We have studied the contribution of higher order corrections of the flavor symmetry breaking in the $A_4$ seesaw model with the supersymmetry. Taking account of possible higher dimensional mass operators, we predict the deviation from the tri-bimaximal lepton mixing for both normal hierarchy and inverted hierarchy of neutrino masses. We have found that the value of $\sin^2 2θ_{23}$ is larger than 0.96 and the upper bound of $\sin^2θ_{13}$ is 0.01. We have also examined the flavor changing neutral current of leptons from the soft SUSY breaking in slepton masses and A-terms within the framework …
It is well known that the tri-bimaximal neutrino mixing pattern V_0 can be derived from a class of flavor models with the non-Abelian A_4 symmetry. We point out that small corrections to V_0, which are inherent in the A_4 models and arise from both the charged-lepton and neutrino sectors, have been omitted in the previous works. We show that such corrections may lead the 3 \times 3 neutrino mixing matrix V to a non-unitary deviation from V_0, but they cannot result in a nonzero value of θ_13 or any new CP-violating phases. Current experimental constraints on the unitarity of V allow us to cons…
Recent neutrino oscillation data hint that the smallest neutrino mixing angle theta_{13} is possible to lie in the range 5^\circ \lesssim θ_{13} \lesssim 12^\circ. We show that reasonable perturbations to the democratic mixing pattern, which is geometrically related to the tri-bimaximal mixing pattern through an equal shift θ_* \simeq 9.7^\circ of two large mixing angles, can naturally produce a nearly tri-bimaximal neutrino mixing matrix V with sufficiently large theta_{13}. Two especially simple but viable scenarios of V are proposed and their phenomenological consequences are discussed.
We study perturbations of exactly tri-bimaximal neutrino mixings under the assumption that they are coming solely from the charged lepton mass matrix. This may be plausible in scenarios where the mass generation mechanisms of neutrinos and charged leptons/quarks have a different origin. As a working hypothesis, we assume mass textures which may be generated by the Froggatt-Nielsen mechanism for the charged lepton and quark sectors, which generically leads to strong hierarchies, whereas the neutrino sector is exactly tri-bimaximal with a mild (normal) hierarchy. We find that in this approach, d…
Tri-bimaximal neutrino mixing may arise from see-saw models based on family symmetry which is spontaneously broken by flavons with particular vacuum alignments. However recent analyses hint that tri-bimaximal mixing may be insensitive to the precise form of vacuum alignment. In this paper we derive approximate analytic results which express the deviations from tri-bimaximal neutrino mixing due to vacuum misalignment. We also relate vacuum misalignment to departures from form dominance, corresponding to deviations from the real orthogonal $R$ matrix, where such corrections are necessary to allo…
Possible alternatives to tri-bimaximal mixing are presented based on other symmetry principles, and their predictions for |U_{e3}|, sin^2 theta_{12} and sin^2 theta_{23} are compared to the present neutrino mixing data. In some cases perturbations are required to give better agreement with the data, and the use of a minimal approach is illustrated. Precise experimental determinations of the mixing parameters will be required to decipher the correct mixing pattern and to pin down the appropriate flavor symmetry.
We study the CP violation in the deviation from the tri-bimaximal mixing (TBM) of neutrinos. We examine non-trivial relations among the mixing angles and the CP violating Dirac phase in the typical four cases of the deviation from the TBM. The first two cases are derived by the additional rotation of the 2-3 or 1-3 generations of neutrinos in the TBM basis. The other two cases are given by the additional rotation of the 1-3 or 1-2 generations of charged leptons with the TBM neutrinos. These four cases predict different relations among three mixing angles and the CP violating Dirac phase. The r…
The neutrino oscillation data are well explained by the tri-bimaximal pattern. Recently it has been shown that also the bimaximal pattern could be a very good starting point in order to describe the lepton mixing. In this paper I review both the flavour structures and then I present an explicit example.
In view of the new data from the Daya Bay and RENO collaborations, King has presented a very natural deformation of tri-bimaximal mixing. Here we show that L/E flatness of the e-like event ratio in the atmospheric neutrino data, when coupled with King's observation that the smallest neutrino mixing angle, θ_{13}, seems to be related to the largest quark mixing angle (the Cabibbo angle θ_C), leads to a CP violating tri-bimaximal-Cabibbo mixing. King's tri-bimaximal-Cabibbo mixing follows as a leading order approximation from our result.
We study the possibility of generating deviations from tri-bimaximal (TBM) neutrino mixing to explain the non-zero reactor mixing angle within the framework of both type I and type II seesaw mechanisms. The type I seesaw term gives rise to the $μ-τ$ symmetric TBM pattern of neutrino mass matrix as predicted by generic flavor symmetry models like $A_4$ whereas the type II seesaw term gives rise to the required deviations from TBM pattern to explain the non-zero $θ_{13}$. Considering extremal values of Majorana CP phases such that the neutrino mass eigenvalues have the structure $(m_1, -m_2, m_3…
We parametrize lepton mixing matrix, known as PMNS matrix, in terms of three parameters which account deviations of three mixing angles from their bi-maximal or tri-bimaximal values. On the basis of this parametrization we can determine corresponding charged lepton mixing matrix in terms of those three parameters which can deviate bi-maximal or tri-bimaximal mixing. We find that the charged lepton mixing matrices which can deviate bi-maximal mixing matrix and tri-bimaximal mixing matrix exhibit similar structures. Numerical analysis shows that these charged lepton mixing matrices are close to …
Inspired by the recent T2K indication of a relatively large theta_{13}, we provide a systematic study of some general modifications to three mostly discussed neutrino mixing patterns, i.e., tri-bimaximal, bimaximal and democratic mixing matrices. The correlation between theta_{13} and two large mixing angles are provided according to each modifications. The phenomenological predictions of theta_{12} and theta_{23} are also discussed. After the exclusion of several minimal modifications, we still have reasonable predictions of three mixing angles in 3 Sigma level for other scenarios.
We explore some ways of minimally modifying the neutrino mixing matrix from tribimaximal, characterized by introducing at most one mixing angle and a CP violating phase thus extending our earlier work. One minimal modification, motivated to some extent by group theoretic considerations, is a simple case with the elements $V_{α2}$ of the second column in the mixing matrix equal to $1/\sqrt{3}$. Modifications by keeping one of the columns or one of the rows unchanged from tri-bimaximal mixing all belong to the class of minimal modification. Some of the cases have interesting experimentally testa…
We study a class of models for tri-bimaximal neutrino mixing in SO(10) grand unified SUSY framework. Neutrino masses arise from both type-I and type-II seesaw mechanisms. We use dimension five operators in order to not spoil tri-bimaximal mixing by means of type-I contribution in the neutrino sector. We show that it is possible to fit all fermion masses and mixings including also the recent T2K result as deviation from the tri-bimaximal.
We propose an extension of tri-bimaximal mixing to include a non-zero reactor angle $θ_{13}$ while maintaining the tri-bimaximal predictions for the atmospheric angle $θ_{23}=45^o$ and solar angle $θ_{12}=35^o$. We show how such tri-bimaximal-reactor mixing can arise at leading order from the(type I) see-saw mechanism with partially constrained sequential dominance. Partially constrained sequential dominance can be realized in GUT models with a non-Abelian discrete family symmetry, such as $A_4$, spontaneously broken by flavons with a particular vacuum alignment.
Recent results from T2K, MINOS and Double CHOOZ all indicate a sizeable reactor angle theta_13 which would rule out conventional tri-bimaximal lepton mixing. However, it is possible to maintain the tri-bimaximal solar and atmospheric mixing angle predictions, theta_12 ~ 35 degrees, theta_23 ~ 45 degrees even for a quite sizeable reactor angle theta_13 ~ 8 degrees, using an ansatz called tri-bimaximal-reactor (TBR) mixing proposed by one of us some time ago. We propose an explicit A4 model of leptons based on the type I seesaw mechanism at both the effective and the renormalisable level which, …
We consider the perturbatively modified tribimaximal (or bimaximal) mixing to estimate the (Dirac-type) CP phase in neutrino mixing matrix. The expressions for the CP phase are derived from the equivalence between the standard parametrization of the neutrino mixing matrix for the Majorana neutrino and modified tribimaximal or bimaximal mixing matrices with appropriate CP phases. Carrying out numerical analysis based on the current experimental results for neutrino mixing angles, we can predict the values of the CP phase for several possible cases.
We study the phenomenological implications of breaking the Tri-Bimaximal (TBM) mixing in such a way that either first or second column of TBM mixing matrix remains invariant. We present two such textures and confront them with the experimental data. We give the predictions of these textures for atmospheric mixing angle $θ_{23}$ and Dirac-type CP violating phase $δ$ that will be measured in the future experiments.
Tri-Bimaximal lepton mixing with A4 semidirect product Z2 x Z2 x Z2
考虑了一个基于A4半直积（Ze x Zmu x Ztau）味对称性的模型，该模型描述了具有两个标量A4-三重态的三重极大轻子混合，它们的真空期望值具有相同的排列.中微子质量是通过有效的五维温伯格算子产生的。带电轻子的质量等级是由额外的Froggatt-Nielsen U（1）味对称性产生的，在这种对称性下，右手轻子是带电的。
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 be…
We examine relation between neutrino oscillation parameters and prediction of lepton flavor violation, in light of deviations from tri-bimaximal mixing. Our study shows that upcoming experimental searches for lepton flavor violation process can provide useful implications for neutrino mass spectrum and mixing angles. With simple structure of heavy right-handed neutrino and supersymmetry breaking sectors, the discovery of tau \to mu gamma decay determines neutrino mass hierarchy if large (order 0.1) reactor angle is established.
General structures of the charged lepton and the neutrino mixing matrices leading to tri-bimaximal leptonic mixing are determined. These are then integrated into an SO(10) model within which detailed fits to fermion masses and mixing angles are given. It is shown that one can obtain excellent fits to all the fermion masses and quark mixing angles keeping tri-bimaximal leptonic mixing intact. Different perturbations to the basic structure are considered and those which can or which cannot account for the recent T2K and MINOS results on the reactor mixing angle $θ_{13}^l$ are identified.
Global fits to neutrino oscillation data are compatible with tri-bimaximal mixing pattern, which predicts $θ_{23} = \fracπ{4}, θ_{12} = \sin^{-1} (\frac{1}{\sqrt{3}})$ and $θ_{13} = 0$. We propose here to parametrize the tri-bimaximal mixing matrix $V_{TBM}$ by its hermitian generator $H_{TBM}$ using the exponential map. Then we use the exponential map to express the deviations from tri-bimaximal pattern by deriving the hermitian matrices $H_{z=0}$ and $H_1$. These deviations might come from the symmetry breaking of the neutrino and charged lepton sectors.
Permutation Symmetry, Tri-Bimaximal Neutrino Mixing and the S3 Group Characters
我们假设轻子味基中的中微子质量矩阵是S3自然表示中的S3群矩阵。这就需要一个中微子被三重混合，正如太阳中微子数据所表明的那样。我们继续假设中微子质量基中的带电轻子质量矩阵是S3类代数的自然表示中的S3类矩阵，从而导致精确的三-双极大混合，这与总体数据相容。的三双极大混合矩阵被认为是密切相关的S3字符表，并正确的S2 C S3表的感应系数，其中S2对应于对称性下的μ-τ交换轻子味基础。
We show that the next-to-leading order corrections in the quark-lepton complementarity are important to explain the observed pattern of neutrino mixing. In particular, the next-to-leading order corrections 1) lead to a deviation of θ_{23} from maximal mixing, 2) reduce the predicted value of $\sin^2 2θ_{13}$ by 9.8%, 3) provide the same value of $\sin^2 θ_{12}$ as that of the tri-bimaximal mixing. This is shown by calculating $\sin^2 2θ_{ij} (i,j=1,2,3)$ to ${\cal O}(λ^6)$ in the framework in which the product of the CKM and PMNS matrices is bimaximal.
We propose a realization of the so-called bimodal/schizophrenic model proposed recently. We assume S4, the permutation group of four objects as flavor symmetry giving tri-bimaximal lepton mixing at leading order. In these models the second massive neutrino state is assumed quasi-Dirac and the remaining neutrinos are Majorana states. In the case of inverse mass hierarchy, the lower bound on the neutrinoless double beta decay parameter m_ee is about two times that of the usual lower bound, within the range of sensitivity of the next generation of experiments.
We present a see-saw $A_4$ model for Tri-Bimaximal mixing which is based on a very economical flavour symmetry and field content and still possesses all the good features of $A_4$ models. In particular the charged lepton mass hierarchies are determined by the $A_4\times Z_4$ flavour symmetry itself without invoking a Froggatt-Nielsen U(1) symmetry. Tri-Bimaximal mixing is exact in leading order while all the mixing angles receive corrections of the same order in next-to-the-leading approximation. As a consequence the predicted value of $θ_{13}$ is within the sensitivity of the experiments whic…
The A4 group stands in the basis of many models that predict Tri-Bimaximal neutrino mixing at leading order. We study the Altarelli-Feruglio A4 symmetry model and show that in order to produce as small value of r_{23} (ratio of mass-squared differences) as measured, it requires fine tuning. This observation is important for an evaluation of the model, since the problem it is trying to solve in the first place is the tuning of the three mixing angles. We get the required level of fine tuning for the model in both its basic form and its seesaw realization.
The lepton flavor mixing matrix having one row or one column in common with the bimaximal mixing up to permutations is still compatible with the present neutrino oscillation data. We provide a thorough exploration of generating such a mixing matrix from $S_4$ family symmetry and generalized CP symmetry $H_{CP}$. Supposing that $S_4\rtimes H_{CP}$ is broken down to $Z^{ST^2SU}_2\times H^ν_{CP}$ in the neutrino sector and $Z^{TST^{2}U}_4\rtimes H^{l}_{CP}$ in the charged lepton sector, one column of the PMNS matrix would be of the form $\left(1/2, 1/\sqrt{2}, 1/2\right)^{T}$ up to permutations, …
