Texture zeroes in neutrino mass matrix $M_ν$ may give us hints about the symmetries involved in neutrino mass generation. We examine the viability of such texture zeroes in a model independent way through a bottom-up approach. Using constraints from the neutrino oscillation data, we develop an analytic framework that can identify these symmetries and quantify deviations from them. We analyze the textures of $M_ν$ as well as those of $M_M$, the mass matrix of heavy Majorana neutrinos in the context of Type-I seesaw. We point out how the viability of textures depends on the absolute neutrino mass scale, the neutrino mass ordering and the mixing angle $θ_{13}$. We also examine the compatibility of discrete flavor symmetries like $μ$--$τ$ exchange and $S_3$ permutation with the current data. We show that the $μ-τ$ exchange symmetry for $M_ν$ can be satisfied for any value of the absolute neutrino mass, but for $M_ν$ to satisfy the $S_3$ symmetry, neutrino masses have to be quasi-degenerate. On the other hand, both these symmetries are currently allowed for $M_M$ for all values of absolute neutrino mass and both mass orderings.
It is shown how to obtain recently-proposed two-zero Majorana mass textures in models with three Higgs triplets with small VEVs and a sufficiently massive triplet Majoron by using abelian discrete symmetries. It is briefly discussed how in SU(5) grand unification where the triplets occur in {\bf 15}'s the neutrino textures can be related to up- and down- quark mass textures.
We assume there to be precisely three left-handed neutrino states whose Majorana masses are generated by an unspecified mechanism. Were CP conserved, the symmetric neutrino mass matrix M would be real and all six of its distinct entries could be experimentally determined. But CP is not conserved so that M is likely to be complex. As a result, not all nine of its convention-independent real parameters can be determined without an appeal to theory. Thus we examine the possibility that a restricted class of neutrino mass matrices may suffice to describe current data, namely those complex symmetri…
We study the invisible Majorana fermions of $χ$ in bottomed baryon decays with flavor-changing neutral currents (FCNCs) based on the model-independent effective Lagrangian between the quarks and invisible particles. From the bounds of the coupling constants extracted from the experiments, we examine the decay branching ratios of $Λ_b\toΛχχ$, $Ξ_b^{0(-)}\toΞ^{0(-)}χχ$, $Λ_b\to n χχ$, $Ξ_b^{-}\to Σ^{-} χχ$, $Ξ_b^{0}\to Σ^{0} χχ$, and $Ξ_b^{0}\to Λχχ$, which can be as large as $6.3,~9.2,~5.7,~5.8,~2.7$, and $1.0\times10^{-5}$ for $m_χ=2$ GeV, respectively. Some of these decays are accessible to t…
We perform a model-independent analysis of the possible residual Klein and generalized CP symmetries associated with arbitrary lepton mixing angles in the case that there are three light Majorana neutrino species. This approach emphasizes the unique role of the Majorana phases and provides a useful framework in which to discuss the origin of the Dirac CP phase in scenarios with spontaneously broken flavor and generalized CP symmetries. The method is shown to reproduce known examples in the literature based on tribimaximal and bitrimaximal mixing patterns, and is used to investigate these issue…
From the new existing data with not vanishing theta13 mixing angle we determine the possible shape of the Majorana neutrino mass matrix. We assume that CP symmetry is broken and all Dirac and Majorana phases are taken into account. Two possible approaches "bottom-up" and "top down" are presented. The problem of unphysical phases is examined in detail.
We give a classification of heavy Majorana neutrino mass matrices with up to three texture zeroes, assuming the Dirac masses of the neutrinos to be of the same form as the ones of the up-quarks in the five texture zero solutions for the quark matrices. This is the case for many unified and partially unified models. We find that it is possible to have solutions which account for the solar and atmospheric neutrino problems as well as the COBE observations simultaneously, and we motivate the existence of such solutions from symmetries.
We constructed rephasing invariant measures of CP violation with elements of the neutrino mass matrix, in the basis in which the charged lepton mass matrix is diagonal. We discuss some examples of neutrino mass matrices with texture zeroes, where the present approach is applicable and demonstrate how it simplifies an analysis of CP violation. We applied our approach to study CP violation in all the phenomenologically acceptable 3-generation two-zero texture neutrino mass matrices and shown that in any of these cases there is only one CP phase which contributes to the neutrino oscillation exper…
The measurements of the neutrino and quark mixing angles satisfy the empirical relations called Quark-Lepton Complementarity. These empirical relations suggest the existence of a correlation between the mixing matrices of leptons and quarks. In this work, we examine the possibility that this correlation between the mixing angles of quarks and leptons originates in the similar hierarchy of quarks and charged lepton masses and the seesaw mechanism type~I, that gives mass to the Majorana neutrinos. We assume that the similar mass hierarchies of charged lepton and quark masses allows us to represe…
In addition to the well established large atmospheric angle, a large solar angle is probably present in the leptonic sector. In the context of the see-saw and by means of a bottom-up approach, we explore which patterns for the Dirac and Majorana right-handed mass matrices provide two large mixings in a robust way and with the minimal amount of tuning. Three favourite patterns emerge, which have a suggestive physical interpretation in terms of the role played by right-handed neutrinos: in both solar and atmospheric sectors, either a single or a pseudo-Dirac pair of right-handed neutrinos domina…
The LEP experiment at CERN provided accurate measurements of the $Z$ neutral gauge boson properties. Although all measurements agree well with the SM predictions, the forward backward asymmetry of the bottom-quark remains almost 3$σ$ away from the SM value. We proposed that this anomaly may be explained by the existence of a new $U(1)_D$ gauge boson, which couples with opposite charges to the right-handed components of the bottom and charm quarks. Cancellation of gauge anomalies demands the presence of a vector-like singlet charged lepton as well as a neutral Dirac (or Majorana) particle that …
We perform a bottom-up search for discrete non-Abelian symmetries capable of quantizing the Cabibbo angle that parameterizes CKM mixing. Given a particular Abelian symmetry structure in the up and down sectors, we construct representations of the associated residual generators which explicitly depend on the degrees of freedom present in our effective mixing matrix. We then discretize those degrees of freedom and utilize the Groups, Algorithms, Programming (GAP) package to close the associated finite groups. This short study is performed in the context of recent results indicating that, without…
It is known that the imposition of a class of residual $Z_2\times Z_2$ symmetries on the neutrino mass matrix $M_ν$ and a residual symmetry $Z_n$ ($n\geq 3$) on the Hermitian combination $M_lM_l^\dagger$ of the charged lepton mass matrix leads to a universal prediction of vanishing Dirac CP phase $δ$ if these symmetries are embedded in $Δ(6 n^2)$ groups and if the leptonic doublets transform as a 3 dimensional irreducible representation of the group. The Majorana phases remain arbitrary but they can also be determined in $Δ(6 n^2)$ by imposing generalized CP symmetry (GenCP) consistent with th…
We propose a simple texture for the right-handed Majorana mass matrix to give a large $ν_μ-ν_τ$ mixing angle and hierarchical left-handed neutrino mass pattern. Consistently with the Dirac mass texture of the quark sector realizing the CKM mixing, this naturally explains the recent experimental results on both the atmospheric neutrino anomaly observed by the Superkamiokande collaboration and the solar neutrino problem. In this texture the right-handed Majorana mass of the third generation is of the order of GUT scale, which is favorable for reproducing the observed bottom-tau mass ratio.
We discuss the fermion mass problem in SUSY GUTs, including such ideas as texture zeroes, and Georgi-Jarlskog textures. We focus on a specific supersymmetric model based on the gauge group $SU(4)\otimes SU(2)_L \otimes SU(2)_R$. In this model the gauge group is broken to that of the standard model at $10^{16}$ GeV, and supersymmetry is broken at low-energy. The model may be regarded as a ``surrogate SUSY GUT'', and has several advantages over the $SU(5)$ and $SO(10)$ SUSY GUTs, such as the absence of the doublet-triplet splitting problem, and a simpler Higgs sector which does not involve any l…
In this work we propose an extension to the Standard Model in which we consider the model 2HDM type-III plus massive neutrinos and the horizontal flavor symmetry $S_{3}$ $(ν$2HDM$\otimes S_3)$. In the above framework and with the explicit breaking of flavor symmetry $S_{3}$, the Yukawa matrices in the flavor adapted basis are represented by means of a matrix with two texture zeroes. Also, the active neutrinos are considered as Majorana particles and their masses are generated through type-I seesaw mechanism. The unitary matrices that diagonalize the mass matrices, as well as the flavor mixing …
Within the framework of a local SU(3) family symmetry model, we report a general analysis of the mechanism for neutrino mass generation and mixing, including light sterile neutrinos. In this scenario, ordinary heavy fermions, top and bottom quarks and tau lepton, become massive at tree level from Dirac See-saw mechanisms implemented by the introduction of a new set of $SU(2)_L$ weak singlet vector-like fermions, U,D,E,N, with N a sterile neutrino. Right-handed and the $N_{L,R}$ sterile neutrinos allow the implementation of a 8x8 general Majorana neutrino mass matrix with four or five massless …
Extensions of the Standard Model with additional U(1) symmetries can describe the hierarchy of fermion masses and mixing angles, including neutrinos. The neutrino masses and mixings are determined up to a discrete ambiguity corresponding to the representation content of the Higgs sector responsible for the Majorana mass matrix. The solar and the atmospheric neutrino deficits as well as the COBE data, may be explained simultaneously in specific schemes motivated by symmetries. Using simple, analytic expressions, it is possible to demonstrate the known effect that for small $\tanβ$, phenomenolog…
We construct a supersymmetric $SO(10) \times U(1)_F$ model of the Yukawa interactions at the grand unification scale from knowledge of a phenomenological set of mass matrices obtained by a previous bottom-up approach. The $U(1)_F$ family symmetry determines the textures for the Majorana and generic Dirac mass matrices, while the $SO(10)$ symmetry relates each particular element of the up, down, neutrino and charged lepton Dirac matrices. The dominant second and third family contributions in the Dirac sector are renormalizable, while the remaining contributions to the Dirac mass matrices are of…
We study the effects of considering nontrivial unphysical lepton sector phases on the group theoretical properties of the flavor and generalized CP symmetry elements in the case where there are three light, distinct Majorana neutrino species. We highlight the similarities and differences between the charged lepton and neutrino sectors and further elucidate the group properties of the flavor and generalized CP symmetry elements. We show how the inclusion of these leptonic phases affects the bottom-up constructions of these symmetry elements and discuss the implications for top-down model buildi…
The generation of the right amount of baryon asymmetry $η$ of the Universe from supersymmetric leptogenesis is studied within the type-I seesaw framework with three heavy singlet Majorana neutrinos $N_i\,\,(i = 1,2,3)$ and their superpartners. We assume the occurrence of four zeroes in the neutrino Yukawa coupling matrix $Y_ν$, taken to be $μτ$ symmetric, in the weak basis where $N_i$ (with real masses $M_i>0$) and the charged leptons $l_α\,\, (α= e,μ,τ)$ are mass diagonal. The quadrant of the single nontrivial phase, allowed in the corresponding light neutrino mass matrix $m_ν$, gets fixed an…
We adopt a bottom-up approach to reconstruct the possible neutrino mass matrix patterns, in the hypothesis that $λ= \sin θ_C$, where $θ_C$ is the Cabibbo angle, is a useful expansion parameter in the neutrino sector as it is in the quark sector. A numerical analysis of these Cabibbo structures shows that an inverted hierarchy spectrum is statistically favored by the neutrino oscillation data. We then discuss how apparently conflicting mass and mixing data for quarks, charged leptons and neutrinos can fit in a unified perspective. We show that large mixing angles can appear through the seesaw m…
A bottom-up approach has been adopted to identify a flavour model that agrees with present experimental measurements. The charged fermion mass hierarchies suggest that only the top Yukawa term should be present at the renormalisable level. Similarly, describing the lightness of the active neutrinos through the type-I Seesaw mechanism, right-handed neutrino mass terms should also be present at the renormalisable level. The flavour symmetry of the Lagrangian including the fermionic kinetic terms and only the top Yukawa is then a combination of $U(2)$ and $U(3)$ factors. Once considering the Majo…
The see-saw mechanism is a very attractive explanation for small neutrino masses, parametrized at the GUT scale by the right-handed Majorana mass matrix, ${\cal M}$, and the neutrino Yukawa matrix, ${\bf Y_ν}$. We show that in a SUSY model with universal soft terms, ${\cal M}$ and ${\bf Y_ν}$ can be calculated from the light neutrino masses, the MNS matrix, and ${\bf Y^{\dagger}_ν} {\bf Y_ν}$, which enters into the left-handed slepton radiative corrections. This suggests that in principle the GUT-scale inputs of the seesaw could be reconstructed from the neutrino and sneutrino mass matrices. W…
We construct an explicit $SO(10) \times U(1)_F$ model of the Yukawa interactions by using as a guide previous phenomenological results obtained from a bottom-up approach to quark and lepton mass matrices. The global $U(1)_F$ family symmetry group sets the textures for the Majorana and generic Dirac mass matrices by restricting the type and number of Higgs diagrams which can contribute to each matrix element, while the $SO(10)$ group relates each particular element of the up, down, neutrino and charged lepton Dirac matrices. The Yukawa couplings and vacuum expectation values associated with pai…
The alternative renormalizable minimal $SO(10)$ model is composed of the Yukawa couplings with $\textbf{10} \oplus \textbf{120}$ Higgs fields, whereas the right-handed (RH) neutrino Majorana masses are generated via the Witten mechanism. The gauge coupling unification is achieved together with a unique pattern of the fermion masses and mixing at the grand unification scale due to additional contributions of vector-like quarks to the standard model renormalization group equations. We perform the fitting of the model to the experimental data of charged fermion masses and the CKM matrix. The best…
If neutrinos are to play a relevant cosmological role, they must be essentially degenerate with a mass matrix of the bimaximal mixing type. We study this scenario in the MSSM framework, finding that if neutrino masses are produced by a see-saw mechanism, the radiative corrections give rise to mass splittings and mixing angles that can accommodate the atmospheric and the (large angle MSW) solar neutrino oscillations. This provides a natural origin for the $Δm^2_{sol} << Δm^2_{atm}$ hierarchy. On the other hand, the vacuum oscillation solution to the solar neutrino problem is always excluded. We…
I review the interpretation of solar and atmospheric neutrino data in terms neutrino oscillations and describe some ways to account for the required neutrino masses and mixing angles from first principles, both within top-down and bottom-up approaches. I also discuss non-oscillation phenomena such as nu-less double beta which may probe the absolute scale of neutrino mass, and also reveal its Majorana nature. I note that leptonic CP violation induced by ``Majorana'' phases drop from oscillations but play a role in the leptogenesis scenario for the baryon asymmetry of the Universe. Direct tests …
We report a global fit of parameters for fermion masses and mixing, including light sterile neutrinos, within a local vector $SU(3)$ family symmetry model. In this scenario, ordinary heavy fermions, top and bottom quarks and tau lepton, become massive at tree level from {\bf Dirac See-saw} mechanisms implemented by the introduction of a new set of $SU(2)_L$ weak singlet vector-like fermions, $U,D,E,N$, with $N$ a sterile neutrino. The $N_{L,R}$ sterile neutrinos allow the implementation of a $8\times 8$ general tree level See-saw Majorana neutrino mass matrix with four massless eigenvalues. He…
We consider realizations of GUT models in F-theory. Adopting a bottom up approach, the assumption that the dynamics of the GUT model can in principle decouple from Planck scale physics leads to a surprisingly predictive framework. An internal U(1) hypercharge flux Higgses the GUT group directly to the MSSM or to a flipped GUT model, a mechanism unavailable in heterotic models. This new ingredient automatically addresses a number of puzzles present in traditional GUT models. The internal U(1) hyperflux allows us to solve the doublet-triplet splitting problem, and explains the qualitative featur…
