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.
We show that in a recently proposed $S_3$ model for tri-bimaximal mixing pattern for neutrinos, CP violating phases in neutrino mixings are directly responsible for lepton asymmetry $ε_\ell$. In the exact tri-bimaximal limit, $ε_\ell$ is proportional to one of the Majorana phases whereas in the presence of small deviations from tri-bimaximal pattern, there are two contributions, one being proportional to the Dirac phase and the other to one of the two Majorana phases. In the second case, $θ_{13}$ is nonzero and correlated with the deviation from maximal atmospheric mixing.
We emphasize that the vanishing of the CP asymmetry in leptogenesis, previously observed for models with tri-bimaximal mixing and family symmetry, may be traced to a property of the type I see-saw mechanism satisfied by such models known as Form Dominance, corresponding to the case of a diagonal Casas-Ibarra R-matrix. Form Dominance leads to vanishing flavour-dependent CP asymmetries irrespective of whether one has tri-bimaximal mixing or a family symmetry. Successful leptogenesis requires violation of Form Dominance, but not necessarily violation of tri bimaximal mixing. This may be achieved …
A possible interplay of both terms in the type II see-saw formula is illustrated by presenting a novel way to generate deviations from exact bimaximal neutrino mixing. In type II see-saw mechanism with dominance of the non-canonical SU(2)_L triplet term, the conventional see-saw term can give a small contribution to the neutrino mass matrix. If the triplet term corresponds to the bimaximal mixing scheme in the normal hierarchy, the small contribution of the conventional see-saw term naturally generates non-maximal solar neutrino mixing. Atmospheric neutrino mixing is also reduced from maximal,…
We propose a particularly economical neutrino mass model, in which there are only two right-handed Majorana neutrinos of ${\cal O}(1)$ TeV and their masses are highly degenerate. Its novel Yukawa-coupling texture together with the seesaw mechanism allows us to achieve the normal neutrino mass hierarchy with $m^{}_1 = 0$ and a nearly tri-bimaximal neutrino mixing pattern with the maximal CP-violating phase: $θ^{}_{23} = π/4$, $|δ| = π/2$ and $\sin^2 θ^{}_{12} = (1 - 2 \tan^2 θ^{}_{13})/3$. One may also obtain the inverted neutrino mass hierarchy with $m^{}_3 = 0$ and the corresponding neutrino …
Current experimental data allow the zero value for one neutrino mass, either m_1 = 0 or m_3 = 0. This observation implies that a realistic neutrino mass texture can be established by starting from the limit (a) m_1 = m_2 = 0 and m_3 \neq 0 or (b) m_1 = m_2 \neq 0 and m_3 = 0. In both cases, we may introduce a particular perturbation which ensures the resultant neutrino mixing matrix to be the tri-bimaximal mixing pattern or its viable variations with all entries being formed from small integers and their square roots. We find that it is natural to incorporate this kind of neutrino mass matrix …
We propose a new $A_4$ model in which both the right-handed neutrinos and right-handed charged leptons transform as $A_4$ singlets. We reproduce tri-bimaximal mixing pattern exactly although the $A_4$ symmetry is broken completely at leading order in both the neutrino and charged lepton sectors. The charged lepton mass hierarchies are controlled by the spontaneous breaking of the flavor symmetry. The light neutrino spectrum is predicted to be of normal type and the lightest neutrino is massless at leading order. Although the reactor angle $θ_{13}$ is expected to be of order $λ^2_c$ from the ne…
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…
We study fermion mass matrices of the cascade form which are compatible with the tri-bimaximal lepton mixing and generation mass hierarchy. The flat-cascade lepton matrices imply a parameter-independent relation among the mixing angles and mass eigenvalues. The relation has several indications that the atmospheric neutrino mixing angle is close to maximal and the other two angles have a correlation independently of neutrino mass eigenvalues. We also discuss phenomenological aspects of the cascade matrices; flavor-violating rare decays of charged leptons, thermal leptogenesis, and leptonic CP v…
We review the application of non abelian discrete groups to the theory of neutrino masses and mixing, which is strongly suggested by the agreement of the Tri-Bimaximal mixing pattern with experiment. After summarizing the motivation and the formalism, we discuss specific models, based on A4, S4 and other finite groups, and their phenomenological implications, including lepton flavor violating processes, leptogenesis and the extension to quarks. In alternative to Tri-Bimaximal mixing the application of discrete flavor symmetries to quark-lepton complementarity and Bimaximal Mixing is also consi…
We propose two Type-II seesaw scenarios for the neutrino mass matrix in the left-right symmetric model, in which the Higgs triplet Yukawa coupling matrix takes the appealing Friedberg-Lee texture. We show that the nearly tri-bimaximal neutrino mixing pattern, which is especially favored by current neutrino oscillation data, can be obtained from both scenarios. We also show that the cosmological baryon number asymmetry can naturally be interpreted in these two scenarios via the flavor-independent leptogenesis mechanism.
We study renormalisation group (RG) corrections relevant for leptogenesis in the case of family symmetry models such as the Altarelli-Feruglio A4 model of tri-bimaximal lepton mixing or its extension to tri-maximal mixing. Such corrections are particularly relevant since in large classes of family symmetry models, to leading order, the CP violating parameters of leptogenesis would be identically zero at the family symmetry breaking scale, due to the form dominance property. We find that RG corrections violate form dominance and enable such models to yield viable leptogenesis at the scale of ri…
If lepton masses and mixings are explained by a flavour symmetry in seesaw model which leads to U_{e3}=0 at leading order, we find that, under reasonable assumptions, a future observation of low energy leptonic CP violation implies, barring accidental cancellations, a lepton asymmetry both in flavoured leptogenesis and in its one-flavour approximation. We explicitly implement this approach with a predictive seesaw model for Tri-Bimaximal Mixing (TBM) and show how cosmological baryon asymmetry can be directly trigged by low energy phases appearing in $U_{e3}$. Thanks to this direct correlation …
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 fact that the data on neutrino mixing are still compatible with a situation where Bimaximal mixing is valid in first approximation and it is then corrected by terms of order of the Cabibbo angle, arising from the diagonalization of the charged lepton masses, we construct a model based on the discrete group S4 where those properties are naturally realized. The model is supersymmetric in 4-dimensions and the complete flavour group is S4 x Z4 x U(1)_FN, which also allows to reproduce the hierarchy of the charged lepton spectrum. The only fine tuning needed in the model is to reprod…
We study how lepton flavor violation (LFV) is related to the reactor angle $θ_{13}$, LHC/dark matter (DM) signal with a successful leptogenesis in a radiative seesaw model through $A_4$ flavor symmetry breaking, in the light of the deviation of tri-bimaximal mixing (TBM) angles and the recent precision oscillation data. To do this, we consider the normal mass spectrum of light neutrino giving a successful leptogenesis at electroweak (EW) scale or more with a relatively large $\sinθ_{13}\simeq{\cal O}(0.1)$, where a successful leptogenesis requires LHC/DM signal $m_{-}\lesssim$ a few keV in our…
We present a model which employs the seesaw mechanism with five right-handed neutrinos, leading to trimaximal and CP-conserving lepton mixing. Tri-bimaximal mixing is a natural limiting case of our model which occurs when one particular vacuum expectation value is real and preserves the mu-tau interchange symmetry of the Lagrangian. Our model allows for leptogenesis even in the case of exact tri-bimaximal mixing.
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.
Tri-bimaximal mixing is a specific lepton mixing ansatz, which has been shown to account very successfully for the established neutrino oscillation data. Working in a particular basis (the `circulant basis'), we identify three independent symmetries of tri-bimaximal mixing, which we exploit to set the tri-bimaximal hypothesis in context, alongside some simple, phenomenologically interesting CP-conserving and CP-violating generalisations.
In view of the recent neutrino oscillation data pointing to a non-vanishing value for the smallest mixing angle ($θ_z$), we derive and find explicit realizations of the $(Z_2)^3$ flavor symmetry which characterizes, for the neutrino mass matrix, uniquely a variant of the tripartite form, originally conceived to lead to the tri-bimaximal mixing with $θ_z=0$, so that to allow now for a non-tri-bimaximal pattern with non-zero $θ_z$. We impose this flavor symmetry in a setting including the charged leptons and we see that it can make room, through higher order terms involving new SM-singlet scalar…
In light of the observation of a relatively large $θ_{13}$, the ever popular Tri-Bimaximal (TBM) neutrino mixing which predicts a vanishing $θ_{13}$ needs modifications. In this paper, we shall discuss the possibility of modifying it in a minimal way to fulfil this task. In the first part, a neutrino mass matrix with three independent parameters, which leads to the TM2 mixing, is obtained by analogy with that for the TBM mixing. In the second part, a model that can realize the TM2 mixing is constructed with flavor symmetries $A_4 \times U(1) \times Z_2 \times Z_2 \times Z_2$. It is the variant…
The related issues of Majorana CP violation in the lepton sector and leptogenesis are investigated in detail in two rather generic supersymmetric models with type I see-saw mechanism of neutrino mass generation and A_4 flavour symmetry, which naturally lead at leading order to tri-bimaximal neutrino mixing. The neutrino sector in this class of models is described at leading order by just two real parameters and one phase. This leads, in particular, to significant low energy constraints on the Majorana phases α_{21} and α_{31} in the PMNS matrix, which play the role of leptogenesis CP violating…
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 point out two simple but instructive possibilities to modify the tri-bimaximal neutrino mixing ansatz, such that leptonic CP violation can naturally be incorporated into the resultant scenarios of nearly tri-bimaximal flavor mixing. The consequences of two new ansaetze on solar, atmospheric and reactor neutrino oscillations are analyzed. We also discuss an interesting approach to construct lepton mass matrices under permutation symmetry, from which one may derive another nearly tri-bimaximal neutrino mixing scenario with no intrinsic CP violation in neutrino oscillations.
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.
Following recent results from the SNO solar neutrino experiment and the K2K long-baseline neutrino experiment, the combined existing data on neutrino oscillations now point strongly to a specific form for the lepton mixing matrix, with effective bimaximal mixing of $ν_μ$ and $ν_τ$ at the atmospheric scale and effective trimaximal mixing for $ν_e$ with $ν_μ$ and $ν_τ$ at the solar scale (hence `tri-bimaximal' mixing). We give simple mass-matrices leading to tri-bimaximal mixing, and discuss its relation to the Fritzsch-Xing democratic ansatz.
The complex Clebsch-Gordon coefficients in the double tetrahedral group T' offers the possibility that CP violation can be entirely geometrical in origin, as pointed out by us recently. In this note, we investigate leptogenesis in a SUSY SU(5) x T' model, which gives rise to realistic quark masses and CKM matrix elements, a near tri-bimaximal neutrino mixing pattern, as well as CP violating measures for all quarks and leptons. In terms of 9 independent parameters in the Yukawa sector, the predicted values of the 22 observables agree with current experimental values, including the recent T2K an…
We discuss a grand unified model based on SUSY SU(5) in extra dimensions and on the flavour group A4xU(1) which, besides reproducing tri-bimaximal mixing for neutrinos with the accuracy required by the data, also leads to a natural description of the observed pattern of quark masses and mixings.
The near maximal value for the atmospheric neutrino mixing angle together with the fact that the solar mixing angle satisfies the relation $\sin^2θ_\odot\simeq {1/3}$ is the basis for the so called tri-bimaximal mixing (tbm) when $θ_{13}=0$. In this note, we explore the possibility that tri-bimaximal mixing is an indication of a softly broken higher leptonic symmetry $S_3$, the permutation of three lepton families that embeds the $μ-τ$ exchange symmetry of leptons.
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, …
The tri-bimaximal mixing is a good approximation for the present data of neutrino mixing angles. The deviation from the tri-bimaximal mixing is discussed numerically in the framework of the A4 model. Values of \tan^2θ_{12}, \sin^2 2θ_{23} and |U_{e3}| deviate from the tri-bimaximal mixing due to the corrections of the vacuum alignment of flavon fields. It is remarked that \sin^2 2θ_{23} deviates scarcely from 1 while \sin^2θ_{12} can deviate from 1/3 considerably and \sinθ_{13} could be near the present experimental upper bound. The CP violating measure J_{CP} and the effective Majorana neutri…
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.
An analysis of the leptonic texture for the new triangular mass matrices has been carried out. In particular, it is shown that both bimaximal and nearly bimaximal solutions for solar and atmospheric neutrino anomalies can be generated within this pattern. We have also derived exact and compact parametrization of the leptonic mixing matrix in terms of the lepton masses and the parameters $α, β'$ and $δ$. A consistency with the CHOOZ reactor result for $V_m{_{13}}$ and a smallness of the Jarlskog's invariant parameter are obtained.
The neutrino oscillation data find a good approximation in the so-called tri-bimaximal pattern. Recently a paper appeared showing that also the bimaximal pattern, which is already ruled out by the measurements, 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 flavour model based on the discrete group S4, in which the PMNS mixing matrix is of the bimaximal form in first approximation and after it receives corrections which bring it in agreement with the data. The resulting spectrum of li…
We consider a model based on A4 semidirect product (Ze x Zmu x Ztau) flavor symmetry for Tri-Bimaximal lepton mixing with two scalar A4-triplets whose vacuum expectation values have the same alignment. Neutrino masses are generated through effective dimension five Weinberg operators. Charged leptons mass hierarchies are generated with an additional Froggatt-Nielsen U(1) flavor symmetry under which right-handed leptons are charged.
We propose a parametrization of the lepton mixing matrix in terms of an expansion in powers of the deviations of the reactor, solar and atmospheric mixing angles from their tri-bimaximal values. We show that unitarity triangles and neutrino oscillation formulae have a very compact form when expressed in this parametrization, resulting in considerable simplifications when dealing with neutrino phenomenology. The parametrization, which is completely general, should help to establish possible relations between the deviations of the reactor, solar and atmospheric mixing angles from their tri-bimax…
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…
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.
It has recently been shown how tri-bimaximal neutrino mixing can be achieved, using the see-saw mechanism with constrained sequential dominance, through the vacuum alignment of a broken non-Abelian gauged family symmetry such as SO(3) or SU(3). Generalising the approach of Altarelli and Feruglio developed for an $A_4$ model we show how the reduction of the underlying symmetry to a discrete subgroup of SO(3) or SU(3) renders this alignment a generic property of such models. This means near tri-bimaximal mixing can be quite naturally accommodated in a complete unified theory of quark and lepton …
The tri-bimaximal mixing matrix is most likely the leading order term in the description of leptonic mixing. We derive deviations from tri-bimaximal mixing(TBM) due to corrections from the charged lepton sector. We assume a decoupled 2-3 symmetry, which is a $Z_2$ symmetry, in the charged lepton sector and another $Z_2$ symmetry in the neutrino sector. The TBM is obtained in the flavor symmetric limit. We consider deviations from the TBM form arising from the breaking of the 2-3 symmetry in the charged lepton sector but do not consider deviations from the breaking of the flavor symmetry in the…
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.
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.
In the light of recent discovery of nonzero $θ_{13}$, we have analyzed the Altarelli-Feruglio $A_4$ flavor symmetry model extended with additional flavon. The inclusion of the new field leads to the deviation from exact tri-bimaximal neutrino mixing pattern in the context of type-I see-saw by producing a nonzero $θ_{13}$ consistent with the recent experimental results at the leading order. A sum rule for light neutrino masses is also obtained in this context. The set-up constraints the two Majorana phases involved in the lepton mixing matrix in terms of $A_4$ parameter space. We have shown tha…
We show that the A4 discrete symmetry that naturally leads to tri-bimaximal neutrino mixing can be simply obtained as a result of an orbifolding starting from a model in 6 dimensions. This particular orbifolding has four fixed points where 4 dimensional branes are located and the tetrahedral symmetry of A4 connects these branes. In this approach A4 appears after the reduction from six to four dimensions as a remnant of the 6D space-time symmetry. A previously discussed supersymmetric version of A4 is reinterpreted along these lines.
We postulate that the neutrino mass matrix in the lepton flavour basis is an S3 group matrix in the natural representation of S3. This immediately requires one neutrino to be trimaximally mixed, as suggested by the solar neutrino data. We go on to postulate that the charged-lepton mass matrix in the neutrino mass-basis is an S3 class matrix in the natural representation of the S3 class-algebra, leading to exact tri-bimaximal mixing, which is compatible with data overall. The tri-bimaximal mixing matrix is seen to be closely related to the S3 character table, and is properly the S2 C S3 table o…
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…
Current experimental data allow the zero value for one neutrino mass, either m_1 =0 or m_3 =0. This observation implies that a realistic neutrino mass texture can be established by starting from the limit (a) m_1 = m_2 =0 and m_3 \neq 0 or (b) m_1 = m_2 \neq 0 and m_3 =0. In both cases, we may introduce a particular perturbation which ensures the resultant neutrino mixing matrix to be the tri-bimaximal mixing pattern or its viable variations. We find that it is natural to incorporate this kind of neutrino mass matrix in the minimal Type-II seesaw model with only one heavy right-handed Majorana…
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 tetrahedron $A_4$ group has been widely used in studying neutrino mixing matrix. It provides a natural framework of model building for the tri-bimaximal mixing matrix. In this class of models, it is necessary to have two Higgs fields, $χ$ and $χ'$, transforming under $A_4$ as 3 with one of them having vacuum expectation values for the three components to be equal and another having only one of the components to be non-zero. These specific vev structures require separating $χ$ and $χ'$ from communicating with each other. The clash of the different vev structures for $χ$ and $χ'$ is the so c…
We determine the symmetry groups under which the charged-lepton and the Majorana-neutrino mass terms are invariant. We note that those two groups always exist trivially, i.e. independently of the presence of any symmetries in the Lagrangian, and that they always have the same form. Using this insight, we re-evaluate the recent claim that, whenever lepton mixing is tri-bimaximal, S_4 is the minimal unique horizontal-symmetry group of the Lagrangian of the lepton sector, with S_4 being determined by the symmetries of the lepton mass matrices. We discuss two models for tri-bimaximal mixing which …
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…
We investigate the theoretical stability of the predictions of tri-bimaximal neutrino mixing with respect to third family wave-function corrections. Such third family wave-function corrections can arise from either the canonical normalisation of the kinetic terms or renormalisation group running effects. At leading order both sorts of corrections can be subsumed into a single universal parameter. For hierarchical neutrinos, this leads to a new testable lepton mixing sum rule 's = r cos delta + 2/3 a' (where s, r, a describe the deviations of solar, reactor and atmospheric mixing angles from th…
We model tri-bimaximal lepton mixing from first principles in a way that avoids the problem of the vacuum alignment characteristic of such models. This is achieved by using a softly broken A4 symmetry realized with an isotriplet fermion, also triplet under A4. No scalar A4-triplet is introduced. This represents one possible realization of general schemes characterized by the minimal set of either three or five physical parameters. In the three parameter versions mee vanishes, while in the five parameter schemes the absolute scale of neutrino mass, although not predicted, is related to the two …
We study the possibility of generating non-zero reactor mixing angle $θ_{13}$ by perturbing the $μ-τ$ symmetric neutrino mass matrix. The leading order $μ-τ$ symmetric neutrino mass matrix originates from type I seesaw mechanism whereas the perturbations to $μ-τ$ symmetry originate from type II seesaw term. We consider four different realizations of $μ-τ$ symmetry: Bimaximal Mixing(BM), Tri-bimaximal Mixing (TBM), Hexagonal Mixing (HM) and Golden Ratio Mixing (GRM) all giving rise to $θ_{13} = 0, θ_{23} = \fracπ{4}$ but different non-zero values of solar mixing angle $θ_{12}$. We assume a mini…
We present a supersymmetric $T_{13}$ model for the tri-bimaximal neutrino mixing, and the complete flavor group is $T_{13}\times Z_{4}\times Z_2$. At leading order, the residual symmetry of the charged lepton sector is $Z_3$, and the $T_{13}$ symmetry is broken completely in the neutrino sector. The charged lepton mass hierarchies are determined by the spontaneous breaking of the flavor symmetry, both the type I see-saw mechanism and the Weinberg operator contribute to generating the light neutrino masses. Tri-bimaximal mixing is exact at leading order while subleading contributions introduce …
Bimaximal (BM) and tri-bimaximal (TB) mixings of neutrinos are two special cases of lepton mixing matrix, which predict the reactor angle $θ_{13}=0$ and the atmospheric angle $\tan^2θ_{23}=1$. Recent precision measurements and global analysis of oscillation parameters, have confirmed a non-vanishing value of $θ_{13}$ as well as deviations of $θ_{12}$ and $θ_{23}$ from their maximal values predicted by BM or TB mixing. In this work we mainly concentrate on $θ_{13}$ and $θ_{23}$ to assign $\sinθ_{13}\neq 0$ and $\tan^2θ_{23}<1$ with the help of charged lepton corrections defined by $U_{PMNS}=U^{…
In this paper, we realize the tri-bimaximal mixing in the lepton sector in the context of minimal seesaw in which only two right-handed neutrinos are introduced, with the discrete group $S4$ as the family symmetry. In order to constrain the form of superpotential, a $Z3$ symmetry is also introduced. In the model, the mass matrices for charged leptons and right-handed neutrinos are diagonal. The unitary matrix that diagonalizes the light Majorana neutrino mass matrix is exact tri-bimaximal at LO, and is corrected by small quantities of $\mathcal{O}(0.01)$ at NLO. The mechanism to get the partic…
We analyze the effects of charged lepton corrections and renormalization group (RG) running on the low energy predictions of theories which accurately predict tri-bimaximal neutrino mixing at the high energy scale. In particular we focus on GUT inspired see-saw models with accurate tri-bimaximal neutrino mixing at the GUT scale, in which the charged lepton corrections are Cabibbo-like and give rise to sum rules valid at the GUT scale. We study numerically the RG corrections to a variety of such neutrino mixing sum rules in order to assess their accuracy and reliability when comparing them to f…
