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 neutrino sector. In particular we find the size of $\sin{θ_{13}}$ to be related to the deviation $\sin{θ_{12}}$ from $\sqrt{1/3}$ while the deviation of $\sin{θ_{23}}$ from its tri-bimaximal value is $ \sim {m_μ \over m_τ}$.
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 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.
In this paper, we show how the mixing angles of the standard parameterization add when multiplying the quark and leptonic mixing matrices, i.e., we derive explicit sum rules for the quark and leptonic mixing angles. In this connection, we also discuss other recently proposed sum rules for the mixing angles assuming bimaximal fermion mixing. In addition, we find that the present experimental and phenomenological data of the mixing angles naturally fulfill our sum rules, and thus, give rise to bilarge or bimaximal fermion mixing.
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.
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 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 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 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…
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^{…
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.
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 construct a model for tri-bimaximal lepton mixing which employs only family symmetries and their soft breaking; neither vacuum alignment nor supersymmetry, extra dimensions, or non-renormalizable terms are used in our model. It is an extension of the Standard Model making use of the seesaw mechanism with five right-handed neutrino singlets. The scalar sector comprises four Higgs doublets and one complex gauge singlet. The horizontal symmetry of our model is based on the permutation group S_3 of the lepton families together with the three family lepton numbers--united this constitutes a symm…
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…
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.
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 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…
We show that in see-saw models with bimaximal lepton mixing at the GUT scale and with zero CP phases, the solar mixing angle theta_{12} generically evolves towards sizably smaller values due to Renormalization Group effects, whereas the evolution of theta_{13} and theta_{23} is comparatively small. The currently favored LMA solution of the solar neutrino problem can thus be obtained in a natural way from bimaximal mixing at the GUT scale. We present numerical examples for the evolution of the leptonic mixing angles in the Standard Model and the MSSM, in which the current best-fit values of the…
We present a type-III version of inverse seesaw or, equivalently an inverse version of type-III seesaw. Naturally small neutrino masses arise at low-scale from the exchange of neutral fermions transforming as hyperchargeless SU(2) triplets. In order to implement tri-bimaximal lepton mixing we supplement the minimal SU(3)xSU(2)xU(1) gauge symmetry with an A4-based flavor symmetry. Our scenario induces lepton flavour violating (LFV) three body decays that can proceed at the tree level, while radiative li to lj gamma decays and mu-e conversion in nuclei are also expected to be sizeable. LFV decay…
We show that not only the hierarchical quark CKM mixing matrix but also the "bimaximal" lepton flavor mixing matrix can be derived from the same mass matrix ansatz based on the broken permutation symmetry, by assuming the hierarchy of neutrino masses to be $m_1\simeq m_2 <<m_3$. We also reproduce the recently measured angle of unitary triangle, $\sin 2β$, as well as all the observed experimental values of $V_{\tiny CKM}$ of the quark CKM matrix. And we predict Jarlskog rephasing invariant quantity, $J_{\tiny CP} \simeq 0.18 \times 10^{-4}$, and the upper bound of the same quantity in the lepto…
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 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 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 …
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 consider charged lepton correction to Tri-bimaximal(TBM) neutrino mixing, defined by the relation $U_{PMNS}=U^{\dagger}_l U_{TB}$ and find possible form of $U_l$ which can impart non-zero value of $\sin θ_{13}$ as well as $\tan^2 θ_{23}<1$, consistent with latest global analysis data. We adopt a new parametrization, other than the standard PDG parametrization, to introduce Dirac CP violating phase $δ$ in the PMNS matrix which is discussed by Fritzsch. Under such charged lepton correction pattern we note that $\tan^2 θ_{12}$ becomes dependent on the CP phase $δ$ from where constraints on $δ$…
Neutrino oscillation experiments (excluding the LSND experiment) suggest a tri-bimaximal form for the lepton mixing matrix. This form indicates that the mixing matrix is probably independent of the lepton masses, and suggests the action of an underlying discrete family symmetry. Using these hints, we conjecture that the contrasting forms of the quark and lepton mixing matrices may both be generated by such a discrete family symmetry. This idea is that the diagonalisation matrices out of which the physical mixing matrices are composed have large mixing angles, which cancel out due to a symmetry…
We demonstrate that only two ansatz can produce the features of the neutrino mixing angles. The first ansatz comes from the quark-lepton grand unification; $ν_{Di} = V_{CKM} ν_α$ is satisfied for left-handed neutrinos, where $ν_{Di}$ are the Dirac mass eigenstates and $ν_α$ are the flavour eigenstates. The second ansatz comes from the assumption; $ν_{Di} = U_{bimaximal} ν_{i}$ is satisfied between the Dirac mass eigenstates $ν_{Di}$ and the light Majorana neutrino mass eigenstates $ν_{i}$, where $U_{bimaximal}$ is the bimaximal mixing matrix. By these two ansatz, the Maki-Nakagawa-Sakata matri…
We propose a novel A4 model in which the Tri-Bimaximal (TB) neutrino mixing and the charged lepton mass hierarchy are reproduced simultaneously. At leading order, the residual symmetry of the neutrino sector is Z2 x Z2 which guarantees the TB mixing without adjusting ad hoc free parameters. In the charged lepton sector, one of the previous Z2 is maximally broken and the resulting mass matrix is nearly diagonal and hierarchical. A natural mechanism for the required vacuum alignment is given with the help of the supersymmetry and an abelian symmetry factor. In our model, subleading effects which…
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 …
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…
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.
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.
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 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.
Two negative signs naturally appear in the $U_{μ1}$ and $U_{τ2}$ elements of the Tri-bimaximal (TBM) matrix for positive values of the mixing angles $θ_{12}$ and $θ_{23}$. Apart from this, in other TBM matrices negative signs are shifted to other elements in each case. They account for positive as well as negative values of $θ_{12}$ and $θ_{23}$. We discuss the sign ambiguity in the TBM matrix and find that the TBM matrices, in fact, can be divided into two groups under certain circumstances. Interestingly, this classification of TBM matrices is accompanied by two different $μ-τ$ symmetric mas…
We propose a new pattern of the neutrino mixing matrix which can be parametrized as the product of an arbitrary Hermitian matrix and the well-known tri-bimaximal mixing matrix. In this scenario, nontrivial values of the smallest neutrino mixing angle θ_13 and the CP-violating phases entirely arise from the non-unitary corrections. We present a complete set of series expansion formulas for neutrino oscillation probabilities both in vacuum and in matter of constant density. We do a numerical analysis to show the non-unitary effects on neutrino oscillations. The possibility of determining small n…
We demonstrate that `Bimaximal + Democratic' type neutrino mass matrix can accommodate the deviation of $θ_\odot$ from its maximal value which referred in the literature as `quark-lepton complementarity' along with the other present day neutrino experimental results, namely, atmospheric, CHOOZ, neutrinoless double beta decay ($ββ_{0ν}$) and result obtained from WMAP experiment. We define a function $χ_p$ in terms of solar and atmospheric neutrino mass squared differences and solar neutrino mixing angle (obtained from different experiments and our proposed texture). The masses and mixing angles…
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 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…
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, …
We propose new classes of models which predict both tri-bimaximal lepton mixing and a right-angled Cabibbo-Kobayashi-Maskawa (CKM) unitarity triangle, alpha approximately 90 degrees. The ingredients of the models include a supersymmetric (SUSY) unified gauge group such as SU(5), a discrete family symmetry such as A4 or S4, a shaping symmetry including products of Z2 and Z4 groups as well as spontaneous CP violation. We show how the vacuum alignment in such models allows a simple explanation of alpha approximately 90 degrees by a combination of purely real or purely imaginary vacuum expectation…
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.
We study the lepton flavor models with the flavor symmetry (Z_N \times Z_N \times Z_N)\rtimes Z_3. Our models predict non-vanishing discrete values of θ_{13} as well as θ_{12} and θ_{23} depending on N. For certain values, our models realize the tri-bimaximal mixing angles with θ_{13}=0. For other values, our models provide with discrete deviation from the tri-bimaximal mixing angles.
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 …
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 briefly discuss the present status of models of neutrino mixing. Among the existing viable options we review the virtues of Bimaximal Mixing (that could be implemented by an $S_4$ discrete symmetry), corrected by terms arising from the charged lepton mass diagonalization. In particular in a GUT formulation the property of quark lepton "weak" complementarity can be naturally realized. We discuss in some detail two new versions of particular GUT models, one based on $SU(5)$ and one on $SO(10)$ and the associated phenomenology. We compare these approaches based on symmetry to models based on c…
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…
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 …
The Tri-bimaximal (TBM) mixing is not accidental if structures of the corresponding leptonic mass matrices follow immediately from certain (residual or broken) flavor symmetry. We develop a simple formalism which allows one to analyze effects of deviations of the lepton mixing from TBM on structure of the neutrino mass matrix and on underlying flavor symmetry. We show that possible deviations from the TBM mixing can lead to strong modifications of the mass matrix and strong violation of the TBM mass relations. As a result, the mass matrix may have an "anarchical" structure with random values o…
The neutrino oscillation data are well explained by the tri-bimaximal pattern. Recently a paper appeared showing 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 model based on the discrete symmetry group S4.
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…
We consider tri-bimaximal lepton mixing within low-scale seesaw schemes where light neutrino masses arise from TeV scale physics, potentially accessible at the Large Hadron Collider (LHC). Two examples are considered, based on the A4 flavor symmetry realized within the inverse or the linear seesaw mechanisms. Both are highly predictive so that in both the light neutrino sector effectively depends only on three mass parameters and one Majorana phase, with no CP violation in neutrino oscillations. We find that the linear seesaw leads to a lower bound for neutrinoless double beta decay while the …
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 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.
The present article is an endeavor to look into some fruitful frameworks based on "Bi-maximal" neutrino mixing, from a model independent stand. The possibilities involving the correction or attenuation of the original BM mixing matrix, followed by GUT-inspired charged lepton correction are invoked. The "symmetry-basis" thus constructed, accentuates some interesting facets such as: a modified QLC relation, $θ_{12}+θ_{c}\approx\fracπ{4}-θ_{13}\cos(nπ-δ_{CP})$, a possible link up between neutrino and charged lepton sectors, $θ_{13}^ν=θ_{12}^{l}\sim\mathcal{O}(θ_{C})$ or that between neutrinos and…
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}.
In light of the latest neutrino oscillation data, we examine whether the leptonic flavor mixing matrix can take on an exact form of tri-bimaximal (TBM), golden-ratio (GR) or bimaximal (BM) mixing pattern at a superhigh-energy scale, where such a mixing pattern could be realized by a flavor symmetry, and become compatible with experimental data at the low-energy scale. Within the framework of the Minimal Supersymmetric Standard Model (MSSM), the only hope for realizing such a possibility is to count on the corrections from the renomalization-group (RG) running. In this work we focus on these ra…
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.
We consider charged Lepton Flavour Violation (LFV) in the Constrained Minimal Supersymmetric Standard Model, extended to include the see-saw mechanism with Constrained Sequential Dominance (CSD), where CSD provides a natural see-saw explanation of tri-bimaximal neutrino mixing. When charged lepton corrections to tri-bimaximal neutrino mixing are included, we discover characteristic correlations among the LFV branching ratios, depending on the mass ordering of the right-handed neutrinos, with a pronounced dependence on the leptonic mixing angle $θ_{13}$ (and in some cases also on the Dirac CP p…
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.
