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.

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.Texture specific mass matrices are known to provide satisfactory explanation of quark mixing phenomenon [1]- [8]. In fact, it has been shown in literature that texture 6 zero Fritzsch mass matrices are completely ruled out [1, 2] while texture 5 zero Fritzsch-like mass matrices may not be completely ruled out [1]- [8]. Similarly, in the context of neutrino oscillation phenomenon, intensive investigations have been carried out using texture specific mass matrices [9]- [53]. In case we have to tackle the larger issue of quark and lepton mixing phenomena at a deeper level, it is perhaps desirable to take into consideration the quark lepton unification hypothesis [54]. This immediately brings forth the issue of finding the simplest texture structures at the leading order, compatible with the quark and lepton mixing phenomena. In view of absence of any theoretical justification for Fritzsch-like mass matrices, it becomes essential from the phenomenological point of view to consider non-Fritzsch like mass matrices for quarks as well as neutrinos. In the case of neutrinos, such an exercise has been done [9], [45]-[53], however, a similar exercise has not been carried out for quarks, therefore it is desirable to carry out detailed investigations for non-Fritzsch like quark mass matrices also.Such an exercise is non trivial as can be seen by consideration of texture 3 zero 1

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 CabibboKobayashi-Maskawa (CKM) matrix V , including |V us | |V cd |, |V cb | |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) offdiagonal elements. The phenomenological consequences of these for the allowed texture content and gross structural features of 'hierarchical' quark mass matrices are addressed from a model-independent prospective under the assumption of factorizable phases in these. The approximate and analytical expressions of the CKM matrix elements are derived and a detailed analysis reveals that such structures are in good agreement with the observed quark flavor mixing angles and the CP-violating phase at the 1σ level and call upon a further investigation of the realization of these structures from a top-down prospective.

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 ν 1 and of s 13 as well as the range of Dirac-like CP violating phase δ l would have implications for the texture specific cases considered here.