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

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 particles, normal hierarchy, inverted hierarchy as well as degenerate neutrinos are ruled out for all combinations of texture 6 zero hermitian mass matrices. §1. IntroductionThe large value of θ 13 determined by the reactor neutrino experiments 1) has not only thrown open the door for search of CP violation in the lepton sector, but has also provided impetus to formulate the theories for understanding the origin of neutrino masses and their mixing. Apart from the recent θ 13 measurement, there also has been considerable progress in the measurement of neutrino mass square differences and mixing angles θ 12 and θ 23 in the last few years. However, not much information is available about the leptonic CP violation phase δ l from the neutrino oscillation data. Also, the absolute neutrino mass scale is still unknown. Further, the presently available neutrino oscillation data does not throw any light on the neutrino mass hierarchy, which may be normal/inverted hierarchy and may even be degenerate. Furthermore, the situation becomes complicated when one realizes that neutrino masses are much smaller than charged fermion masses as well as it is yet not clear whether neutrinos are Dirac or Majorana particles.In the absence of a convincing fermion flavor theory, several approaches have been considered to understand fermion mass generation problem, e.g., texture zeros, 2) seesaw mechanism, 3) radiative mechanisms, 4) flavor symmetries, 5) extra dimensions, 6) etc.. In this context, texture specific mass matrices have received a good deal of attention in the literature, in particular, Fritzsch-like texture specific mass matrices seem to be very helpful in understanding the pattern of quark mixings and CP violation. 7)-9) Taking clues from the success of these matrices in the context of quarks, several attempts have been made to consider texture specific lepton mass matrices 10)-14) for explaining the pattern of neutrino masses and mixings. In the absence of a sufficient amount of data regarding neutrino masses and mixings, it would require a very careful scrutiny of all possible textures to find viable structures, which are compatible with data and theoretical ideas, so that these are kept in mind while formulating mass matrices at the grand unified theory (GUT) scale.In the quark sector, both Fritzsch like as well as non Fritzsch like texture six zero mass matrices have been completely ruled out. 9) In leptonic sector, most of the analyses hav...

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