Investigating Non-Fritzsch-Like Texture Specific Quark Mass Matrices

Abstract

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

Possible Textures of the Fermion Mass Matrices

“…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, for details see [27,31]. 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, details can be found in [14,22].…”

Five texture zeros andCPviolation for the standard model quark mass matrices

“…Four and six texture zeros imply one and three physical relationships respectively, and allow us to write one or the three mixing angles as functions of the six quarks masses and the CP violation phase. But six texture zeros are already ruled out by analytic and numerical considerations [18,19]. 5.…”

“…As it has been shown in several places, the parallel and non-parallel six texture zeros does not work properly and it has been ruled out by analytic [18] and numeric [19] studies (only a charm quark mass half of its measured value can rescue this "anzätze").…”

On the four-zero texture of quark mass matrices and its stability

“…The Fritzsch ansatz totally involves eight independent parameters, and thus it can predict two relations among six quark masses and four flavor mixing parameters. However, it has been shown that this simple ansatz is in conflict with current experimental data [6].…”