Texture Zeros Research Articles

A unified model of quarks and leptons with a universal texture zero

We show that a universal texture zero in the (1,1) position of all fermionic mass matrices, including heavy right-handed Majorana neutrinos driving a type-I see-saw mechanism, can lead to a viable spectrum of mass, mixing and CP violation for both quarks and leptons, including (but not limited to) three important postdictions: the Cabibbo angle, the charged lepton masses, and the leptonic ‘reactor’ angle. We model this texture zero with a non-Abelian discrete family symmetry that can easily be embedded in a grand unified framework, and discuss the details of the phenomenology after electroweak and family symmetry breaking. We provide an explicit numerical fit to the available data and obtain excellent agreement with the 18 observables in the charged fermion and neutrino sectors with just 9 free parameters. We further show that the vacua of our new scalar familon fields are readily aligned along desired directions in family space, and also demonstrate discrete gauge anomaly freedom at the relevant scale of our effective theory.

Texture zero neutrino models and their connection with resonant leptogenesis

Within the low scale resonant leptogenesis scenario, the cosmological CP asymmetry may arise by radiative corrections through the charged lepton Yukawa couplings. While in some cases, as one expects, decisive role is played by the λτ coupling, we show that in specific neutrino textures only by inclusion of the λμ the cosmological CP violation is generated at 1-loop level.With the purpose to relate the cosmological CP violation to the leptonic CP phase δ, we consider an extension of MSSM with two right handed neutrinos (RHN), which are degenerate in mass at high scales. Together with this, we first consider two texture zero 3×2 Dirac Yukawa matrices of neutrinos. These via see-saw generated neutrino mass matrices augmented by single ΔL=2 dimension five (d=5) operator give predictive neutrino sectors with calculable CP asymmetries. The latter is generated through λμ,τ coupling(s) at 1-loop level. Detailed analysis of the leptogenesis is performed. We also revise some one texture zero Dirac Yukawa matrices, considered earlier, and show that addition of a single ΔL=2, d=5 entry in the neutrino mass matrices, together with newly computed 1-loop corrections to the CP asymmetries, give nice accommodation of the neutrino sector and desirable amount of the baryon asymmetry via the resonant leptogenesis even for rather low RHN masses (∼few TeV–107 GeV).

Texture zeros and hierarchical masses from flavour (mis)alignment

We introduce an unconventional interpretation of the fermion mass matrix elements. As the full rotational freedom of the gauge-kinetic terms renders a set of infinite bases called weak bases, basis-dependent structures as mass matrices are unphysical. Matrix invariants, on the other hand, provide a set of basis-independent objects which are of more relevance. We employ one of these invariants to give a new parametrisation of the mass matrices. By virtue of it, one gains control over its implicit implications on several mass matrix structures. The key element is the trace invariant which resembles the equation of a hypersphere with a radius equal to the Frobenius norm of the mass matrix. With the concepts of alignment or misalignment we can identify texture zeros with certain alignments whereas Froggatt–Nielsen structures in the matrix elements are governed by misalignment. This method allows further insights of traditional approaches to the underlying flavour geometry.

Lepton CP violation in a ν2HDM with flavor

In this work we propose an extension to the Standard Model in which we consider a type-III two-Higgs-doublet model (2HDM) plus massive neutrinos and the horizontal flavor symmetry ${S}_{3}$ ($\ensuremath{\nu}2\mathrm{HDM}\ensuremath{\bigotimes}{S}_{3}$). 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 zeros. Also, the active neutrinos are considered as Majorana particles and their masses are generated through the type-I seesaw mechanism. The unitary matrices that diagonalize the mass matrices, as well as the flavor-mixing matrices, are expressed in terms of fermion mass ratios. Consequently, in the mass basis the entries of the Yukawa matrices naturally acquire the form of the so-called Cheng-Sher ansatz. For the leptonic sector of $\ensuremath{\nu}2\mathrm{HDM}\ensuremath{\bigotimes}{S}_{3}$, we compare, through a ${\ensuremath{\chi}}^{2}$ likelihood test, the theoretical expressions of the flavor-mixing angles with the masses and flavor-mixing leptons current experimental data. The results obtained in this ${\ensuremath{\chi}}^{2}$ analysis are in very good agreement with the current experimental data. We also obtain allowed value ranges for the ``Dirac-like'' phase factor, as well as for the two Majorana phase factors. Furthermore, we study the phenomenological implications of these numerical values of the $CP$-violation phases on the neutrinoless double-beta decay, and for long baseline neutrino oscillation experiments such as T2K, $\mathrm{NO}\ensuremath{\nu}\mathrm{A}$, and DUNE.

Exploring the predictability of symmetric texture zeros in quark mass matrices

The predictability of hierarchical quark mass matrices with symmetrically placed texture zeros is explored in the light of current precision measurements on quark masses and mixing data and interesting phenomenological relations among the quark mass ratios and flavor mixing angles along with CP asymmetry angle $\beta$ are deduced for different predictive textures within the framework of the Standard Model. It is shown that a single non-trivial phase in these mass matrices is sufficient enough to account for the observed CP-violation in the quark sector. In particular, it is observed that the Cabibbo angle is predominantly determined by the ratio $\sqrt{m_{d}/m_{s}}$ and corrections may also result from $\sqrt{m_{u}/m_{c}}$. Furthermore, $V_{cb}\cong \sqrt{m_d/m_b}$ or $V_{cb}\cong \sqrt{m_c/2m_t}$ along with $V_{ub}\simeq \sqrt{m_u/m_t}$ provide excellent agreements with the current mixing data and $\beta =-Arg\lbrace V_{td}\rbrace$ may provide a rigorous test at the B-factories for some of these texture zero structures.

The neutrino flavor puzzle

The neutrino flavor puzzle

Probing Majorana neutrino textures at DUNE

We study the possibility of probing different texture zero neutrino mass matrices at long baseline neutrino experiment DUNE. Assuming a diagonal charged lepton basis and Majorana nature of light neutrinos, we first classify the possible light neutrino mass matrices with one and two texture zeros and then numerically evaluate the parameter space in terms of atmospheric mixing angle $\theta_{23}$ and Dirac CP phase $\delta_{\text{CP}}$ which satisfies the texture zero conditions. We then feed these parameter values into the numerical analysis in order to study the sensitivity of DUNE experiment to them. We find that the DUNE will be able to exclude some of these texture zero mass matrices which restrict the $(\theta_{23}-\delta_{\text{CP}})$ to a very specific range of values.

Study of texture zeros of fermion mass matrices in minimal extended seesaw mechanism and symmetry realization

In our work, we study the texture zeros of [Formula: see text] in the minimal extended type-I seesaw (MES) with incorporating one extra gauge singlet field “[Formula: see text]”. The MES models deal with the Dirac neutrino mass matrix [Formula: see text], the right-handed Majorana mass matrix [Formula: see text] and the sterile neutrino mass matrix [Formula: see text]. We carry out the mapping of all possible zero textures of [Formula: see text], [Formula: see text] and [Formula: see text] for phenomenologically predictive cases having total eight zeros of [Formula: see text] and [Formula: see text] studied in the literature. With this motivation, we consider (a) [Formula: see text] scheme, (b) [Formula: see text] scheme and (c) [Formula: see text] scheme, where the digits of a pair represent the number of zeros of [Formula: see text] and [Formula: see text], respectively along with the one zero and two zero textures of [Formula: see text]. There are a large number of possibilities of zeros of fermion mass matrices but the implementation of [Formula: see text] transformations reduces it to a very minimum number of basic structures. Interestingly out of four allowed one zero textures of [Formula: see text] without sterile neutrino, only three cases ([Formula: see text], [Formula: see text] and [Formula: see text]) are allowed in MES mechanism for the [Formula: see text] and [Formula: see text] schemes. We find some correlations for different combination of [Formula: see text], [Formula: see text] and [Formula: see text] on enforcement of zeros. We examined all the correlations under the recent neutrino oscillation data and find that only [Formula: see text] survives while both [Formula: see text] and [Formula: see text] are ruled out. Interestingly the one zero textures inherently represent the inverted hierarchy of the mass ordering of light neutrinos. No two zero textures of [Formula: see text] survive in MES although there are a number of allowed structures phenomenologically. The allowed texture zeros are finally realized using a discrete Abelian flavor symmetry group [Formula: see text] with the extension of standard model to include some scalar fields.

Implications of texture zeros for a variant of tribimaximal mixing

We study the phenomenological implications of the presence of two texture zeros in the neutrino mass matrix assuming that the neutrino mixing matrix has its first column identical to that of the tribimaximal mixing matrix. Only two patterns of this kind are compatible with the experimental data. These textures have definite predictions for the neutrino observables that are testable in future neutrino experiments.

Obtaining nonvanishing 𝜃13 with constrained neutrino Yukawa matrix and implications for flavor model buildings

Assuming a diagonal Majorana neutrino mass matrix, we investigate the neutrino Yukawa textures which lead to a nonzero reactor mixing angle [Formula: see text]. The neutrino effective coupling matrix [Formula: see text] is pre-diagonalized by a constant mixing pattern [Formula: see text] with a vanishing [Formula: see text]. The resulting pre-diagonal symmetrical matrix [Formula: see text] is set to be four texture zeros with two types of off-diagonal elements nonzero, which are [Formula: see text] and [Formula: see text], respectively. With the expectation of simple textures, we thoroughly classify the linear combinations, [Formula: see text], [Formula: see text] and [Formula: see text] of Yukawa elements [Formula: see text] in the same row, according to the values, vanishing or not. Each set of the classifications can lead to a Yukawa texture which may have implications for the discrete flavor model buildings. We also present a model based on [Formula: see text] according to one set of the constraints on the three combinations with a specific choice of a coefficient in Yukawa texture.

Maximally restrictive leptonic texture zeros in two-Higgs-doublet models

The implementation of maximally restrictive texture zeros in the leptonic sector is investigated in the context of two-Higgs-doublet models with Majorana neutrinos. After analyzing all maximally restrictive pairs of leptonic mass matrices with zero entries, we conclude that there are only four texture combinations that are compatible with observations at 3σ confidence level and can be implemented through Abelian symmetries in a two-Higgs-doublet model. The compatibility of these textures with current constraints on lepton-flavor-violating processes is also studied. The ultraviolet completion of these models is discussed in the framework of the seesaw mechanism for neutrino masses.

Phenomenological study of extended seesaw model for light sterile neutrino

We study the zero textures of the Yukawa matrices in the minimal extended type-I seesaw (MES) model which can give rise to ∼ eV scale sterile neutrinos. In this model, three right handed neutrinos and one extra singlet S are added to generate a light sterile neutrino. The light neutrino mass matrix for the active neutrinos, mν, depends on the Dirac neutrino mass matrix (MD), Majorana neutrino mass matrix (MR) and the mass matrix (MS) coupling the right handed neutrinos and the singlet. The model predicts one of the light neutrino masses to vanish. We systematically investigate the zero textures in MD and observe that maximum five zeros in MD can lead to viable zero textures in mν. For this study we consider four different forms for MR (one diagonal and three off diagonal) and two different forms of (MS) containing one zero. Remarkably we obtain only two allowed forms of mν (meτ = 0 and mττ = 0) having inverted hierarchical mass spectrum. We re-analyze the phenomenological implications of these two allowed textures of mν in the light of recent neutrino oscillation data. In the context of the MES model, we also express the low energy mass matrix, the mass of the sterile neutrino and the active-sterile mixing in terms of the parameters of the allowed Yukawa matrices. The MES model leads to some extra correlations which disallow some of the Yukawa textures obtained earlier, even though they give allowed one-zero forms of mν. We show that the allowed textures in our study can be realized in a simple way in a model based on MES mechanism with a discrete Abelian flavor symmetry group Z8 × Z2.

Texture zeros in neutrino mass matrix

The Standard Model does not explain the hierarchy problem. Before the discovery of nonzero lepton mixing angle {\theta}13 high hopes in explanation of the shape of the lepton mixing matrix were combined with non abelian symmetries. Nowadays, assuming one Higgs doublet, it is unlikely that this is still valid. Texture zeroes, that are combined with abelian symmetries, are intensively studied. The neutrino mass matrix is a natural way to study such symmetries.

Perturbed Yukawa textures in the minimal seesaw model

We revisit the minimal seesaw model, i.e., the type-I seesaw mechanism involving only two right-handed neutrinos. This model represents an important minimal benchmark scenario for future experimental updates on neutrino oscillations. It features four real parameters that cannot be fixed by the current data: two CP -violating phases, δ and σ, as well as one complex parameter, z, that is experimentally inaccessible at low energies. The parameter z controls the structure of the neutrino Yukawa matrix at high energies, which is why it may be regarded as a label or index for all UV completions of the minimal seesaw model. The fact that z encompasses only two real degrees of freedom allows us to systematically scan the minimal seesaw model over all of its possible UV completions. In doing so, we address the following question: suppose δ and σ should be measured at particular values in the future — to what extent is one then still able to realize approximate textures in the neutrino Yukawa matrix? Our analysis, thus, generalizes previous studies of the minimal seesaw model based on the assumption of exact texture zeros. In particular, our study allows us to assess the theoretical uncertainty inherent to the common texture ansatz. One of our main results is that a normal light-neutrino mass hierarchy is, in fact, still consistent with a two-zero Yukawa texture, provided that the two texture zeros receive corrections at the level of mathcal{O} (10%). While our numerical results pertain to the minimal seesaw model only, our general procedure appears to be applicable to other neutrino mass models as well.

Zero textures and vanishing minor in neutrino mass models and their minimal symmetry realization.

We have made a systematical texture study on some neutrino mass models (Singh 1 et al.,2002; Singh 2 et al., 2002) which are based on diagonal charged lepton mass matrices (M l ) and Dirac neutrino mass matrices (M D ). We investigate the zero textures of the Majorana mass matrix (M R ). Interestingly we find that all the M R ’s corresponds to only one zero textures. We also observe that the one zero texture of M R propagate to the left-handed neutrino mass matrices as their vanishing minors. We perform a minimal realization of the textures under the context of an Abelian symmetric group. However in doing so, we have extended the SM to include some SU(2) singlet scalar.

Proposed Economical and Stable Lepton Mass Matrices with Texture Zeros

There are many viable combinations of texture zeros in lepton mass matrices. We propose an economical and stable mass texture. Analytical and numerical results on mixing parameters and the effective mass of neutrinos are obtained. These results satisfy new constraints from neutrinos oscillation experiments and cosmological observations. Their stabilities are also examined through the perturbations to some structure parameters. Our proposition reveals that, in the complex forest of neutrinos mixing models, a simple and stable one is still possible.

More about unphysical zeroes in quark mass matrices

We look for all weak bases that lead to texture zeroes in the quark mass matrices and contain a minimal number of parameters in the framework of the standard model. Since there are ten physical observables, namely, six nonvanishing quark masses, three mixing angles and one CP phase, the maximum number of texture zeroes in both quark sectors is altogether nine. The nine zero entries can only be distributed between the up- and down-quark sectors in matrix pairs with six and three texture zeroes or five and four texture zeroes. In the weak basis where a quark mass matrix is nonsingular and has six zeroes in one sector, we find that there are 54 matrices with three zeroes in the other sector, obtainable through right-handed weak basis transformations. It is also found that all pairs composed of a nonsingular matrix with five zeroes and a nonsingular and nondecoupled matrix with four zeroes simply correspond to a weak basis choice. Without any further assumptions, none of these pairs of up- and down-quark mass matrices has physical content. It is shown that all non-weak-basis pairs of quark mass matrices that contain nine zeroes are not compatible with current experimental data. The particular case of the so-called nearest-neighbour-interaction pattern is also discussed.

Implication of θ13 on Majorana Neutrino mass matrices with One Texture Zero and One Vanishing Eigenvalue

The latest neutrino mixing data has established the relatively large value of reactor mixing angle, θ13 ∼90. In view of that and assuming Majorana nature of neutrinos, we have reexamined the texture one-zero neutrino mass matrices with one vanishing neutrino mass in the flavor basis. We observe that for m1 = 0 (Normal mass ordering), all the six one zero classes are now phenomenologically ruled out and for m3 = 0 (Inverted mass ordering), only four classes out of total six are viable with the latest neutrino oscillation data at 3σ confidence level.

Edge of a cliff

We discuss the neutrino flavor structures in the Occam's razor approach for the Dirac neutrino mass matrices. We assume that the charged lepton mass matrix takes a diagonal base, while the right-handed Majorana neutrino mass matrix is also diagonal and we consider nine patterns of the four zero textures for the Dirac neutrinos mass matrices. We numerically analyze the left-handed Majorana neutrino mass matrices for nine patterns of the Dirac neutrino mass matrices and we found two interesting patterns where both normal and inverted neutrino mass hierarchies can be realized. We also found if the neutrino mass is normal hierarchy, this scenario will be likely to be excluded by the measurements of the Dirac CP violating phase in the T2K and NO$\nu $A neutrino experiments, for instance. On the other hand, if the neutrino mass is inverted hierarchy, this scenario will be also likely to be excluded by the measurements of neutrinoless double beta decay experiments, e.g., KamLAND-Zen experiment.

Probing maximal zero textures with broken cyclic symmetry in inverse seesaw

Within the framework of inverse seesaw mechanism we investigate neutrino mass matrices invariant under cyclic symmetry (Z3) with maximal zero texture (6 zero textures). We explore two different approaches to obtain the cyclic symmetry invariant form of the constituent matrices. In the first one we consider explicit cyclic symmetry in the neutrino sector of the Lagrangian which dictates the emerged effective neutrino mass matrix (mν) to be symmetry invariant and hence leads to a degeneracy in masses. We then consider explicit breaking of the symmetry through a dimensionless parameter ϵ′ to remove the degeneracy. It is seen that the method doesn't support the current neutrino oscillation global fit data even after considering the correction from cyclic symmetry invariant charged lepton mass matrix (ml) unless the breaking parameter is too large. In the second method, we assume the same forms of the neutrino mass matrices, however, symmetry is broken in the charged lepton sector. All the structures of the mass matrices are now dictated by an effective residual symmetry of some larger symmetry group in the Lagrangian. For illustration, we exemplify a toy model based on softly broken A4 symmetry group which leads to one of the combinations of ml, mD, MRS and μ to generate effective mν. All the emerged mass matrices predict a constraint range of the CP violating phases and atmospheric mixing angle along with an inverted hierarchical structure of the neutrino masses. Further, significant predictions on ββ0ν decay parameter |m11| and the sum of the three light neutrino masses (Σimi) are also obtained.