A detailed investigation of all possible textures of Fritzsch-like and non-Fritzsch like, 144 for texture 6 zero and 432 for texture 5 zero mass matrices, have been carried out to ascertain their compatibility with the existing quark mixing data. It seems that all the texture 6 zero possibilities are completely ruled out whereas in the case of texture 5 zero mass matrices the only viable possibility looks to be that of Fritzsch-like.
In the Standard Model, we obtain a non-Fritzsch like configuration with five texture zeros for the quark mass matrices. This matrix generates the quark masses, the inner angles of the CKM unitary triangle, and the CP-violating phase in the quark sector. This work can be applied to the PMNS matrix in the lepton sector, by assuming Dirac masses for the neutrinos, where non-trivial predictions for the neutrino masses and mixing angles are expected.
From mass textures point of view, we present a comparative study of the $\mathbf{S}_{3}$ flavor symmetry in the left-right symmetry model (LRSM) and the baryon minus lepton model (BLM) taking into account their predictions on the CKM mixing matrix. To do this, we recover the already studied quark mass matrix, that comes from some published papers, and under certain strong assumption, one can show that there are predictive scenarios in the LRSM and BLM where the modified Fritzsch and nearest neighbor interaction (NNI) textures drive respectively the quark mixings. As main result, the CKM mixing…
Implications of the lepton mixing angles, in particular of theta_13, have been investigated for minimal as well as non-minimal Fritzsch-like textures for the case of Majorana neutrinos. Both, in minimal texture (texture 6 zero lepton mass matrices) and non-minimal textures (two cases of texture 5 zero lepton mass matrices), inverted hierarchy and degenerate scenario of neutrino masses have been ruled out. The implications of theta_13 have been investigated on the lightest neutrino mass m_ν_1 as well as the effective Majorana mass m_ee.
对于Majorana中微子和Dirac中微子，利用具有平行织构结构的Fritzsch织构4零质量矩阵和Dirac中微子质量矩阵（M_{νD}），对中微子质量的正态/反转层次以及简并情形进行了详细的预测.在3 σ C. L时，似乎排除了颠倒的等级以及退化的情况。马约拉纳中微子和狄拉克中微子。对于正规阶谱，计算了Jarlskog的再定相不变参数J、CP破坏类Dirac相δ和中微子有效质量m_{ee}.在这种情况下，m_{ν_1}和θ_{13}的下限将对中微子的性质产生影响。
Texture specific fermion mass matrices have played an important role in understanding several features of fermion masses and mixings. In the present work, we have given an overview of all possible cases of Fritzsch-like as well as non Fritzsch-like texture 6 and 5 zero fermion mass matrices. Further, for the case of texture 4 zero Fritzsch-like quark mass matrices, the issue of the hierarchy of the elements of the mass matrices and the role of their phases have been discussed. Furthermore, the case of texture 4 zero Fritzsch-like lepton mass matrices has also been discussed with an emphasis on…
We show that non-Hermitian and nearest-neighbor-interacting perturbations to the Fritzsch textures of lepton and quark mass matrices can make both of them fit current experimental data very well. In particular, we obtain θ_{23} \simeq 45^\circ for the atmospheric neutrino mixing angle and predict θ_{13} \simeq 3^\circ to 6^\circ for the smallest neutrino mixing angle when the perturbations in the lepton sector are at the 20% level. The same level of perturbations is required in the quark sector, where the Jarlskog invariant of CP violation is about 3.7 \times 10^{-5}. In comparison, the streng…
We present an extension of the Standard Model (SM) based on the discrete flavor symmetry S3 which gives a neutrino mass matrix with two-zero texture of Fritzsch-type and nearly diagonal charged lepton mass matrix. The model is compatible with the normal hierarchy only and predicts the sine squared of the reactor angle to be 0.01 at the best fit values of solar and atmospheric parameters and maximal leptonic CP violation.
A comprehensive review of several aspects of fermion mixing phenomenon and texture specific mass matrices have been presented. Regarding fermion mixings, implications of unitarity and certain new developments for the CKM paradigm have been discussed. In the leptonic sector, the question of possibility of CP violation has been discussed in detail from the unitarity triangle perspective. In the case of texture specific mass matrices, the issues of viability of Fritzsch-like as well as non Fritzsch-like mass matrices have been detailed for both the quark and leptonic sectors. The relationship of …
Texture six zero Fritzsch like as well as non Fritzsch like hermitian lepton mass matrices (144 combinations in all) have been investigated for both Majorana and Dirac neutrinos for their compatibility with the current neutrino oscillation data, keeping in mind the hierarchy of neutrino masses. All the combinations considered here for Majorana neutrino masses are ruled out by the existing data in the case of inverted hierarchy and degenerate scenario. For Majorana neutrinos with normal hierarchy, only 16 combinations can accommodate the experimental data. Assuming neutrinos to be Dirac particl…
The issue of texture specific mass matrices has been discussed by incorporating Weak Basis transformations and the concept of `naturalness'. Interestingly, we find that starting from the most general mass matrices, one can arrive at texture four zero mass matrices which can fit both quark as well as lepton mixing data and are similar to the original Fritzsch ansatze.
We respond to the comments of S. Sharma et al. [Phys. Rev. D 91, 038301 (2015)] on my recent paper, Y. Giraldo [Phys. Rev. D 86, 093021 (2012)]. In their comments, they begin discussing a particular class of five-zero texture non-Fritzsch-like quark mass matrix, which was proposed by me, and questioning its validity. Then, they put in doubt the phases included in the unitary matrices used for diagonalizing the quark mass matrices, from which they claim that the CP violating parameter $ε_k$ obtained does not agree with the experimental value. Because of these comments, finally, they recommend b…
Implications of recently measured leptonic mixing angle $θ_{13}$ as well as the other two mixing angles have been examined for Fritzsch-like mass matrices with minimal texture for Dirac neutrinos. Interestingly, the existing data seems to rule out this texture specific case of Dirac neutrinos for normal, inverted hierarchy as well as degenerate scenario of masses.
Implications of texture specific mass matrices have been investigated for both quarks and neutrinos. Interestingly, for the case of quarks Fritzsch-like texture 4 zero mass matrices have been found to be compatible with the present precisely known sin2βas well as other precise CKM matrix elements. In the case of leptonic mass matrices, for both Majorana and Dirac neutrinos we find that for texture 4, 5, 6 zero mass matrices the inverted hierarchy and degenerate scenarios of neutrino masses are ruled out by the present data.
Considering Dirac neutrinos and Fritzsch-like texture 6 zero and 5 zero mass matrices, detailed predictions for cases pertaining to normal/inverted hierarchy as well as degenerate scenario of neutrino masses have been carried out. All the cases considered here pertaining to inverted hierarchy and degenerate scenario of neutrino masses are ruled out by the existing data. For the normal hierarchy cases, the lower limit of m_nu_1 and of s_13 as well as the range of Dirac-like CP violating phase delta_l would have implications for the texture specific cases considered here.
In pursuance of finding a viable set of mass matrices, keeping in mind recent precision measurement of quark masses and CKM parameters, we have carried out a detailed and comprehensive analysis of hermitian texture 4 zero quark mass matrices. Our analysis reveals that only Fritzsch like texture 4 zero combination provides a viable set of mass matrices for the present quark mixing data and all other texture 4 zero combinations are ruled out. A good number of these possibilities can be ruled out analytically, the other possibilities are excluded by the present quark mixing data. Interestingly, o…
In the context of Fritzsch-like texture 4 zero Hermitian quark mass matrices, we have attempted to find an `exact' formula for sin2βwherein the dependence of βon the quark masses and the elements of the quark mass matrices is visible in a simple and clear manner. This has been achieved keeping in mind the strong hierarchy of the quark masses and assuming the weak hierarchy amongst the elements of the mass matrices. This `exact' formula represents a vast improvement over the leading order formula based on strong hierarchy of the elements of the mass matrices. Apart from showing the compatibilit…
We propose a simple extension of the electroweak standard model based on the discrete $S_3$ symmetry that is capable of realizing a nearly minimal Fritzsch-type texture for the Dirac mass matrices of both charged leptons and neutrinos. This is achieved with the aid of additional $Z_5$ and $Z_3$ symmetries, one of which can be embedded in $U(1)_{B-L}$. Five complex scalar singlet fields are introduced in addition to the SM with right-handed neutrinos. Although more general, the modified texture of the model retains the successful features of the minimal texture without fine-tuning; namely, it a…
In the light of several recent analyses pointing towards texture 4-zero Fritzsch-like quark mass matrices as the only viable structures for quark mass matrices, this work adopts a model independent approach to reconstruct an alternate and simplified structure of texture specific quark mass matrices in a generalized 'u-diagonal' basis within the Standard Model framework using the Unitarity of CKM matrix and the observed hierarchies in quark mass spectra and mixing angles. It is observed that the measured 1$σ$ values of the three physical parameters namely $m_{\rm{u}}$, $m_{\rm{d}}$ and $s_{12}$…
We construct a multiscalar and non-renormalizable model where the $\mathbf{S}_{3}$ flavor symmetry drives mainly the Yukawa couplings. In the quark sector, the Nearest Neighbor Interaction (NNI) textures are behind the CKM mixing matrix so that this is fitted in good agreement with the last available results. In the lepton sector, an almost diagonal charged lepton mass matrix and extended Fritzsch mass textures in the effective neutrino mass matrix, that comes from the type II see-saw mechanism, provide consistent values for the mixing angles where the normal hierarchy is favored. The model pr…
Fermion masses and mixing from an extra gauge symmetry
假设一个水平阿贝尔（规范）对称性是在原点的纹理零的费米子质量矩阵，我们展示了如何现实的质量模式可以产生的标量场的真空期望值的存在下，打破额外的$U(1)$对称性。在最简单的情况下，只有一对单态场，在L-R对称性的假设下，我们得到夸克质量矩阵{ \it à la Fritzsch}。$U(1)$对称性可以通过格林-施瓦兹机制变得无反常，在这种情况下，规范耦合的正则统一作为其副产品出现。中微子质量的产生需要两个额外的重标量（希格斯）场来确定右手中微子质量矩阵的纹理结构，或者后者将包含一个层次的尺度。
Fritzsch-Xing matrices are a particular class of texture 4 zero hermitian quark mass matrices, known to be successful in accommodating the quark mixing data. In the present work, it is shown that these texture 4-zero matrices with only one phase parameter, unlike the usually considered two phase parameters, are not only consistent with the latest experimental quark mixing data, but also predict the CP violation parameters, $J$ and corresponding phase $δ$, in agreement with the recent global analyses. We also show that the mass matrix elements do not exhibit a strong hierarchy and there is a st…
In this work we have investigated the phenomenological consequences of two-zero textures of \textit{inverse} neutrino mass matrix ($M_ν^{-1}$) in light of the large mixing angle (LMA) and large mixing angle-\textit{dark} (LMA-D) solutions, later of which originates if neutrinos exhibit non-standard interactions with matter. Out of fifteen possibilities, only seven two-zero textures of $M_ν^{-1}$ are found to be phenomenologically allowed under LMA and/or LMA-D descriptions. In particular, five textures are in consonance with both LMA and LMA-D solutions and are necessarily $CP$ violating while…
We study the hierarchy of quark masses and mixings in a model based on a 5-dimensional spacetime with constant curvature of Randall-Sundrum type with two branes, where the Electroweak Symmetry Breaking is caused dynamically by the condensation of a 4th generation of quarks, due to underlying physics from the 5D bulk and the first KK gluons. We first study the hierarchy of quark masses and mixings that can be obtained from purely adjusting the profile localizations, finding that realistic masses are not reproduced unless non trivial hierarchies of underlying 4-fermion interactions from the bulk…
In this paper, we extend the Fritzsch ansatz of quark mass matrices while retaining their hierarchical structures and show that the main features of the Cabibbo-Kobayashi-Maskawa (CKM) matrix $V$, including $|V^{}_{us}| \simeq |V^{}_{cd}|$, $|V^{}_{cb}| \simeq |V^{}_{ts}|$ and $|V^{}_{ub}|/|V^{}_{cb}| < |V^{}_{td}|/|V^{}_{ts}|$, can be well understood. This agreement is observed especially when the mass matrices have non-vanishing $(1,3)$ and $(3,1)$ off-diagonal elements. The phenomenological consequences of these for the allowed texture content and gross structural features of `hierarchical'…
In a renormalizable $SO(10)$ theory, all fermion mass matrices are linear combinations of three fundamental types, $M^{10}, M^{\overline{126}}$, and $M^{120}$, whose superscripts indicate their $SO(10)$ transformation properties. We point out that each of these fundamental mass matrices possesses a natural symmetry that can be used to generate an unbroken horizontal symmetry $\G$, if the natural symmetry is taken to be the residual symmetry. This built-in symmetry is a Coxeter group. If it is finite, it must be one of five groups, $S_4,\ Z_2\x S_4$,\ $Z_2\x A_5$, plus two `rank-4' groups. Thes…
The lepton sector is studied within a flavored non-renormalizable model where the $\mathbf{S}_{3}\otimes \mathbf{Z}_{2}$ flavor symmetry drives the Yukawa couplings. In this framework, the effective neutrino mass, that comes from the type II see-saw mechanism, as well as the charged lepton mass matrices are hierarchical and possessed (under a benchmark in the charged sector) a kind of Fritzsch textures that achieve to accommodate the mixing angles in good agreement with the last experimental data. The model predicts a CP-violating phase consistent with the experimental data and the branching r…
In the scenario with four generation quarks and leptons and using a 3 + 1 neutrino model having one sterile and the three standard active neutrinos with a $4 \times 4$ unitary transformation matrix, $U_{PMNS_{4}}$, we perform a model-based analysis using the latest global data and determine bounds on the sterile neutrino parameters i.e. the neutrino mixing angles. Motivated by our previous results, where, in a quark-lepton complementarity (QLC) model we predicted the values of $θ_{13}^{PMNS}=(9_{-2}^{+1})^{\circ}$ and $θ_{23}^{PMNS}=(40.60_{-0.3}^{+0.1})^{\circ}$. In the QLC model the non-triv…
Investigating the CKM matrix in different parametrization schemes, it is noticed that those schemes can be divided into a few groups where the sine values of the CP phase for each group are approximately equal. Using those relations, several approximate equalities among the elements of CKM matrix are established. Assuming them to be exact, there are infinite numbers of solutions and by choosing special values for the free parameters in those solutions, several textures presented in literature are obtained. The case can also be generalized to the PMNS matrix for the lepton sector. In parallel, …
