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Without adhering to any specific model, we have presented 4 X 4 quark mixing matrix as an extension of the 3 X 3 PDG parametrization of the CKM matrix. Using unitarity constraints as well as the hierarchy among the elements of the 3 X 3 CKM matrix, we have found the hierarchy among the 4th row and 4th column elements of the 4 X 4 quark mixing matrix. Further, for the fourth generation case, we have explicitly found the 9 independent rephasing invariant parameters J_4X4. Also, using phenomenological estimates of the 4th row and 4th column elements, we have numerically evaluated these 9 parameters., Comment: 16 pages

The hierarchy amongst the CKM matrix elements, highlighted recently by Luo and Xing, has been rigorously revisited using the PDG parameterization incorporating unitarity constraints. Further, we have explored the evaluation of the CP violating parameter \epsilon_k for the 9 possible unitarity ensured equivalent independent parametrizations of CKM matrix. Interestingly, we find that not all of these reproduce the value of parameter \epsilon_k, this being presumably due to the hierarchical nature of the CKM matrix elements. This situation is echoing similar conclusions regarding the evaluation of Jarlskog's rephasing invariant parameter J through unitarity ensured equivalent possibilities., Comment: 13 pages. arXiv admin note: text overlap with arXiv:2310.11152

Using unitarity, unlike the approaches available in the literature, we have constructed 9 independent representations of CKM matrix starting with each of the 9 elements of the matrix. The relationship of these independently constructed representations with the already available ones in the literature has been compared and discussed. Further, the implications of these representations have been explored for some of the CKM parameters such as \delta, J and \epsilon_k. Interestingly, we find that the PDG representation which is equivalent to our first representation seems to be most appropriate to incorporate the hierarchy of the elements of the CKM matrix as well as to describe the related phenomenology., Comment: 19 pages, 1 figure, accepted for publication in PTEP

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, our conclusions remain valid, even if in future there are perturbations in the ranges of the light quark masses or CKM parameters., Comment: 22 pages, 12 figures

An attempt has been made to carry out a detailed analysis of quark mass matrices having structure beyond the minimal texture. In particular, keeping in mind, precision measurements of CKM parameters as well as refinements in the ranges of light quark masses, we have examined the viability of all possible combinations of hermitian texture 5 zero quark mass matrices. Interestingly, one finds that all these possibilities are now excluded by the present quark mixing data, thereby, having important implications for model building., Comment: 14 pages, 10 figures. arXiv admin note: text overlap with arXiv:1911.08835

We have carried out an extensive analysis of all possible minimal texture quark mass matrices implying 169 texture 6 zero combinations. One finds that all these combinations are ruled out, a good number of these analytically, the other possibilities are excluded by the present quark mixing data. Interestingly, even if in future, there are changes in the ranges of the light quark masses, these conclusions remain valid., Comment: 16 pages, 12 figures,accepted for publication in PTEP

The issue of texture specific fermion mass matrices have been examined briefly from the `bottom-up' perspective. In case no conditions are imposed, the texture ansatze leads to a large number of viable possibilities. However, besides textures, if in case one incorporates the ideas of `natural mass matrices' and uses the facility of Weak Basis Transformations, then one is able to arrive at a minimal finite set of viable mass matrices in the case of quarks., Comment: 8 pages, 1 figure

The present work attempts to provide an overview of texture specific lepton mass matrices. In particular, we summarize the findings of some recent analyses carried out within non flavor basis, wherein a parallel texture structure for the lepton and neutrino mass matrices is considered., Comment: 9 pages

In the light of refined and large reactor mixing angle $\theta_{13}$, we have revisited the texture three and two zero neutrino mass matrices in the flavor basis. For Majorana neutrinos, it has been explicitly shown that all the texture three zero mass matrices remain ruled out. Further, for both normal and inverted mass ordering, for the texture two zero neutrino mass matrices one finds interesting constraints on the Dirac-like CP violating phase $\delta$ and Majorana phases $\rho$ and $\sigma$., Comment: 12 pages, 9 figures

Starting with the most general mass matrices, within the context of Standard Model and some of its extensions, incorporating the ideas of weak basis transformations and naturalness, we find that there exists a particular set of texture specific quark mass matrices which can be considered to be the minimal viable option., Comment: To appear in the proceedings of XXI DAE-BRNS High Energy Physics Symposium, IIT Guwahati, India, December 2014, based closely on arXiv:1503.03963, arXiv:1404.5726

Within the Standard Model, starting with the most general mass matrices we have used the facility of making weak basis transformations and have imposed the condition of `naturalness' to carry out their analysis within the texture zero approach. Interestingly, our analysis reveals that a particular set of texture 4 zero quark mass matrices can be considered to be a unique viable option for the description of quark mixing data., Comment: 9 pages, 2 figures

Recently, using specific Weak Basis transformations, Y. Giraldo [Phys. Rev. D 86, 093021 (2012)] has constructed some texture 5 and 4 zero quark mass matrices and examined their compatibility with the quark mixing data. In this comment, we have re-analyzed these to bring forth certain important issues regarding their viability which need to be taken note of., Comment: 5 pages, 1 figure, Accepted for publication in PRD

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., Comment: 14 pages, 2 figures

In the light of the recent measurement of the leptonic mixing angle $\theta_{13}$, implications of the latest mixing data have been investigated for non-minimal textures of lepton mass matrices assuming the neutrinos to be Majorana like. Large number of possible texture specific lepton mass matrices have been examined for their compatibility with the lepton mixing data in the case of normal hierarchy, inverted hierarchy and degenerate scenario of neutrino masses. Specifically, apart from other phenomenological quantities the implications of the lepton mixing angle $\theta_{13}$ have been investigated on the lightest neutrino mass as well as the effective Majorana mass $$., Comment: 28 pages, 26 figures. arXiv admin note: substantial text overlap with arXiv:1402.0628

In the light of the recent measurement of the leptonic mixing angle $\theta_{13}$, implications of the latest mixing data have been investigated for non-minimal textures of lepton mass matrices pertaining to Dirac neutrinos. All these texture specific lepton mass matrices have been examined for their compatibility with the latest data in the cases of normal hierarchy, inverted hierarchy and degenerate scenario of neutrino masses. The implications of all the three lepton mixing angles have been investigated on the lightest neutrino mass as well as the Jarlskog's CP violating parameter in the leptonic sector., Comment: 38 pages, 46 figures

Implications of recently measured leptonic mixing angle $\theta_{13}$ 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., Comment: 11 pages, 2 figures, Accepted for publication in PTEP. arXiv admin note: text overlap with arXiv:0904.4534

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 textures, naturalness and weak basis rotations has also been looked into. The issue of the compatibility of texture specific mass matrices with the SO(10) based GUT mass matrices has also been discussed., Comment: 100 pages, 19 figures

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_\nu_1 as well as the effective Majorana mass m_ee., Comment: 18 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:hep-ph/0607074, arXiv:hep-ph/0703005, arXiv:0904.4534

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 the hierarchy of neutrino masses for both Majorana and Dirac neutrinos., Comment: 21 pages, 3 figures

In view of the latest T2K and MINOS observations regarding the mixing angle s_{13}, we have explored the possibility of existence of CP violation in the leptonic sector. Using hints from the construction of the 'db' unitarity triangle in the quark sector, we have made an attempt to construct the '\nu_1.\nu_3' leptonic unitarity triangle, suggesting a good possibility of having non zero CP violation., Comment: 8 pages, 2 figures

We have attempted to extend the parameter space of the elements of the texture 4 zero Hermitian quark mass matrices, to include the case of `weak hierarchy' amongst them along with the usually considered `strong hierarchy' case. This has been carried out by giving wide variation to the hierarchy defining parameters D_U and D_D, having implications for the structural features of the mass matrices. We find that not only the weakly hierarchical mass matrices are able to reproduce the strongly hierarchical mixing angles but also both the phases having their origin in the mass matrices have to be non zero to achieve compatibility of these matrices with recent quark mixing data. Further noting the difference between the exclusive and inclusive values of V_ub, we have carried out separate analyses corresponding to these., Comment: 13 pages, 4 figures, version accepted for publication in Journal Of Physics G

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 sin2\beta as 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., Comment: 8 pages, 1 figure

In the context of Fritzsch-like texture 4 zero Hermitian quark mass matrices, we have attempted to find an `exact' formula for sin2\beta wherein the dependence of \beta on 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 compatibility of texture 4 zero mass matrices with the present value of sin2\beta and other CKM parameters, we find interesting conclusions regarding the structural features of the mass matrices., Comment: One reference added. Accepted for publication in Physics Letters B

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., Comment: 21 pages, 5 figures, Accepted for publication in Physical Review D

For Majorana or Dirac neutrinos, using Fritzsch-like texture 4 zero mass matrices with parallel texture structures for the charged leptons and the Dirac neutrino mass matrix (M_{\nu D}), detailed predictions for cases pertaining to normal/inverted hierarchy as well as degenerate scenarios of neutrino masses have been carried out. The inverted hierarchy as well as degenerate scenarios seem to be ruled out at 3 \sigma C.L. for both Majorana and Dirac neutrinos. For normal hierarchy, Jarlskog's rephasing invariant parameter J, the CP violating Dirac-like phase \delta and the effective neutrino mass m_{ee} have been calculated. For this case, lower limits of m_{\nu_1} and \theta_{13} would have implications for the nature of neutrinos., Comment: 15 pages, 3 figures, minor changes in figures and text

Following analogy of the `db' triangle in the quark mixing case, we have explored the construction of the `\nu_2.\nu_3' leptonic unitarity triangle using the Maki-Nakagawa-Sakata matrix obtained by Bjorken {\it et al.} through generalization of the tribimaximal scenario. In particular, for the U_{e3} range 0.05-0.15, the existence of the leptonic unitarity triangle indicates a fairly good possibility of having non zero CP violation., Comment: 8 pages, 2 figures

The CKM and PMNS matrices have been constructed based on the latest measurements, largely free from theoretical inputs as well as likely NP effects in the case of the former. To facilitate the construction of the CKM matrix in the PDG representation as well as in view of the comparatively large error in the measured value of the CP violating phase \delta, the possibility of its construction from the tree level measured CKM elements has also been explored using the unitarity triangle. In view of the persistent difference between the |V_{ub}| exclusive and inclusive values, we have carried out separate analyses corresponding to these. The PMNS matrix has been constructed by incorporating the constraints due to solar and atmospheric neutrinos as well as by giving full variation to the Dirac-like CP violating phase \delta and considering different values of s_{13} having implications for different models of lepton mass matrices. Taking clue from quark mixing phenomenology, an analogous analysis of the leptonic unitarity triangle allows an estimate of the likely presence of CP violation in the leptonic sector., Comment: 11 pages, 2 figures

Unitarity along with precision measurements of sin2\beta, V_{us} and V_{cb} allows one to find a lower bound V_{ub}\geq 0.0035 which, on using the recently measured angle \alpha of the unitarity triangle, translates to V_{ub}= 0.0035\pm 0.0002. This precise value, stable for a good deal of changes in \alpha, along with CP violating phase \delta found from unitarity allows the construction of a `precise' CKM matrix. The above unitarity based value of V_{ub} is in agreement with the latest exclusive value used as input by UTfit, CKMfitter, HFAG, however underlines the so called `tension' faced by the latest inclusive V_{ub}=0.00449 \pm 0.00033. Further, using this inclusive value of V_{ub} along with the latest sin2\beta, one finds \delta=23 ^{\rm o}- 39 ^{\rm o}, again in conflict with \delta measured in B-decays. The calculated ranges of the elements of the CKM matrix are in excellent agreement with those obtained recently by UTfit, CKMfitter and HFAG. Also, the ratio \frac{V_{ts}}{V_{td}} is in agreement with its latest measured value, whereas there is some disagreement between the `measured' and the calculated V_{td} values., Comment: 10 pages, 1 figure, incorporated latest data

Using seesaw mechanism and Fritzsch-like texture 6 zero and 5 zero lepton Dirac 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 would have implications for the texture 6 zero and texture 5 zero cases considered here., Comment: 13 pages, 4 figures. Small changes to the previous version and a new reference added

Lepton mass matrices similar to texture 4 zero quark mass matrices, known to be quite successful in explaining the CKM phenomenology, have been considered for finding the mixing matrix element U_{e3} (\equiv s_{13}) respecting the CHOOZ constraint, with s_{12} and \Delta m_{12}^2 constrained by SNP and s_{23} and \Delta m_{23}^2 constrained by ANP. Taking charged lepton mass matrix M_l to be diagonal, we find that the ranges of s_{13} corresponding to different SNP solutions very well include the corresponding values of s_{13} found by Akhmedov et al. by considering neutrino mass matrix M_{\nu} with no texture zeros. Considering M_l and M_{\nu} both to be real and non-diagonal, s_{13} ranges for the four SNP solutions come out to be: \sim 0-0.19 (LMA), 0.038-0.093 (SMA), 0.042-0.095 (LOW), 0.038-0.096 (VO) which remain of the same order when M_l and M_{\nu} are considered to be complex and non-diagonal., Comment: 13 pages, LaTeX

The recently reanalysed LSND data is investigated in the context of three flavor oscillations, with an emphasis on mass hierarchies and $s_{13}$. The resultant mass hierarchies and oscillation angles are tested with regard to "key" features of solar neutrinos and atmospheric neutrinos, e.g., "average" survival probability in the case of solar neutrinos, and zenith angle dependence and up-down asymmetry in the case of high energy atmospheric neutrinos. We find there are three distinct mass hierarchies, e.g., $\Delta m << \Delta M, \Delta m < \Delta M$ and $\Delta m \simeq \Delta M$. In the first and second case, the calculated range of $s_{13}$ is in agreement with the "LMA" solution of Akhmedov {\it et al.}, the lower limit on $s_{13}$ in these cases is also in agreement with the recent analysis of Garcia {\it et al.} based on the constraints of SNP, ANP and CHOOZ, therefore, strongly supporting the neutrino oscillations observed at LSND. Further, the solutions of $s_{13}$ found in the third case correspond to the value of $s_{13}$ found by Akhmedov {\it et al.} in the case of "SMA" and "LOW" solutions. A rough estimate of the possibility of the existence of CP violation in the leptonic sector is also carried out for different possible ranges of $s_{13}$, indicating that the CP asymmetries may be measureable even in the case of LSND., Comment: 16 pages, LaTex, 1 eps figure, Minor changes in the text