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.
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 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.
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…
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.
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.
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.
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 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.
The recent measurements of the neutrino reactor angle require a re-examination of flavour models based on discrete groups. Indeed, when these models deal with the Tri-Bimaximal, the Bimaximal and the Golden Ratio mixing patterns, some tensions arise in order to accommodate the reactor angle. In particular, strong constraints come from lepton flavour violating processes, like mu -> e gamma. We present the analysis and the main results.
In this talk neutrino mass models are reviewed and the impact of a non-zero reactor angle and other deviations from tri-bimaximal mixing are discussed. We propose some benchmark models, where the only way to discriminate between them is by high precision neutrino oscillation experiments.
Recently T2K gives hint in favor of large reactor angle. Most of the models, with tri-bimaximal mixing at the leading order, can not reproduce such a large mixing angle since they predict typically corrections for the reactor angle of the order of the Cabibbo angle. In this letter, we discuss the possibility to have large reactor angle within the T2K region with maximal atmospheric mixing angle and trimaximal solar mixing angle, through the deviation from tri-bimaximal. We derive the structure of neutrino mass matrix that leads to the large reactor angle leaving maximal atmospheric angle and t…
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.
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…
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.
The recent results from T2K and MINOS experiments point towards a relatively large value of the reactor angle θ_13 in the lepton sector. In this paper we show how a large θ_13 can arise from the charged lepton sector alone in the context of an SU(5) GUT. In such a scenario (tri-)bimaximal mixing in the neutrino sector is still a viable possibility. We also analyse the general implications of the considered scenario for the searches of CP violation in neutrino oscillations.
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.
Parametrization of the quark and lepton mixing matrices is the first attempt to understand the mixing of fermions. In this work, we parameterize the quark and lepton matrices with the help of quark-lepton complementarity (QLC) in a tri-bimaximal pattern of lepton mixing matrix. In this way, we combine the parametrization of the two matrices with each other. We apply this new parametrization to several physical quantities, and show its simplicity in the expression of, e.g., the Jarlskog parameter of CP violation.
It is shown that empirical relations between the charged lepton spectra and the quark spectra together with a bimaximal or near bimaximal neutrino mixing matrix necessarily imply that there is a contribution to U(e3) given by thetaC/3/sqrt(2) ~ sqrt(m_{e}/2m_{mu}) ~ 0.052, where thetaC is the Cabibbo angle. This prediction could be tested in the near future reactor experiments. The charged lepton mixing also generates a less robust prediction for the angle theta(23) and a small contribution to the phase delta.
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…
Current experimental data on neutrino oscillations are consistent with the tri-bimaximal mixing. If future experimental data will determine a non-zero $V_{e3}$ and/or find CP violations in neutrino oscillations, there is the need to modify the mixing pattern. We find that a simple neutrino mass matrix, resulting from $A_4$ family symmetry breaking with residual $Z_3$ and $Z_2$ discrete symmetries respectively for the Higgs sectors generating the charged lepton and neutrino mass matrices, can satisfy the required modifications. The neutrino mass matrix is minimally modified with just one additi…
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.
Recent measurements of the lepton mixing angle $θ_{13}$ by the Daya Bay and RENO reactor experiments are consistent with the relationship $θ_{13}\approx θ_C/\sqrt{2}$ where $ θ_C$ is the Cabibbo angle. We propose Tri-bimaximal-Cabibbo (TBC) mixing, in which $\sin θ_{13}= \sin θ_C/\sqrt{2}$, $\sin θ_{23}= 1/\sqrt{2}$ and $\sin θ_{12}= 1/\sqrt{3}$. We show that TBC mixing may arise approximately from Tri-bimaximal, Bi-maximal or Golden Ratio neutrino mixing, together with Cabibbo-like charged lepton corrections arising from a Pati-Salam gauge group, leading to predictions for the CP-violating ph…
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.
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 discuss consequences of combining the effective $Z_2\times Z_2$ symmetry of the tri-bimaximal neutrino mass matrix with the CP symmetry. Imposition of such generalized $Z_2\times Z_2$ symmetries leads to predictive neutrino mass matrices determined in terms of only four parameters and leads to non-zero $θ_{13}$ and maximal atmospheric mixing angle and CP violating phase. It is shown that an effective generalized $Z_2\times Z_2$ symmetry of the mass matrix can arise from the $A_4$ symmetry with specific vacuum alignment. The neutrino mass matrix in the considered model has only three real pa…
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.
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^{…
We study the stability of the Harrison-Perkins-Scott (HPS) mixing pattern, assumed to hold at some high energy scale, against supersymmetric radiative corrections. We work in the framework of a reference minimal supergravity model (mSUGRA) where supersymmetry breaking is universal and flavor-blind at unification. The radiative corrections considered include both RGE running as well as threshold effects. We find that in this case the solar mixing angle can only increase with respect to the HPS reference value, while the atmospheric and reactor mixing angles remain essentially stable. Deviations…
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…
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.
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…
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 neutrino mixing matrix is expanded in powers of a small parameter $λ$ in tri-bimaximal mixing pattern. We also present some applications of this parametrization, such as to the expression of the Jarlskog parameter $J$. Comparing with other parametrizations (such as the parametrization in bimaximal mixing pattern), this parametrization converges more quickly, but is of less symmetry.
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 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.
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.
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.
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…
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…
In this work we analyze the corrections to tribimaximal (TBM), bimaximal (BM) and democratic (DC) mixing matrices for explaining large reactor mixing angle $θ_{13}$ and checking the consistency with other neutrino mixing angles. The corrections are parameterized in terms of small orthogonal rotations (R) with corresponding modified PMNS matrix of the form $R_{ij}\cdot U \cdot R_{kl}$ where $R_{ij}$ is rotation in ij sector and U is any one of these special matrices. We showed the rotations $R_{13}\cdot U \cdot R_{23}$, $R_{12}\cdot U \cdot R_{13}$ for BM and $R_{13}\cdot U \cdot R_{13}$ for TB…
The long baseline neutrino experiment, T2K, and the reactor experiment, Double Chooz will soon present new data. If we expect $\sinθ_{13}$ to be 0.1-0.2, which is close to the present experimental upper bound, we should not persist in the paradigm of the tri-bimaximal mixing. We discuss breaking the tri-bimaximal mixing by adding a simple mass matrix, which could be derived from some non-Abelian discrete symmetries. It is found that $\sinθ_{13}=0.1-0.2$ is expected in our model independent analysis of the generalized mass matrix for the normal or inverted hierarchical neutrino mass spectrum. O…
We investigate deviation from the tri-bimaximal mixing in the case of ultra high energy neutrino using ICECUBE detector. We consider the ratio of No. of muon tracks to the shower generated due to eletrons and hadrons. Our analysis shows for tri-bimaximal mixing the ratio comes out around 4.05. Keeping $θ_12$ and $θ_23$ fixed at tri-bimaximal value, we have varied the angle $θ_{13}$ = $3^o$, $6^o$, $9^o$ and the value of the ratio gradually decreases. The variation of ratio lies 8% to 18% from the tri-bimaximal mixing value.
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…
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 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…
An attempt is made to explore the possibility for deviations of solar mixing angle ($θ_{12}$) from tri-bimaximal mixings, without sacrificing the predictions of maximal atmospheric mixing angle ($θ_{23}=π/4$) and zero reactor angle ($θ_{13}=0$). We find that the above conjecture can be automatically realised in the inverted hierarchical neutrino mass model having 2-3 symmetry, in the basis where charged lepton mass matrix is diagonal. For the observed ranges of $\bigtriangleup m^2_{21}$ and $\bigtriangleup m^2_{23]$, we calculate the predictions on $\tan^2θ_{12}=0.5, 0.45, 0.35$ for different …
We investigate in a model-independent way to what extent one can perturb tri-bimaximal mixing in order to generate a sizable value of |U_{e3}|, while at the same time keeping solar neutrino mixing near its measured value, which is close to sin^2 theta_{12} = 1/3. Three straightforward breaking mechanisms to generate |U_{e3}| of about 0.1 are considered. For charged lepton corrections, the suppression of a sizable contribution to sin^2 theta_{12} can be achieved if CP violation in neutrino oscillations is almost maximal. Generation of the indicated value of |U_{e3}| of about 0.1 through renorma…
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.
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…
