Exploring the parameter space of texture four-zero quark mass matrices

Abstract

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.

Possible Textures of the Fermion Mass Matrices

“…Further, for the case of texture 4 zero quark mass matrices [14,22], including the case of 'weak hierarchy' along with the usually considered 'strong hierarchy' case, one finds that the weakly hierarchical mass matrices are able to reproduce the strongly hierarchical mixing angles. Also, both the phases having their origin in the mass matrices have to be non zero to achieve compatibility of these matrices with the quark mixing data.…”

“…As an extension of texture 5 zero mass matrices, several authors [9,12]- [14] carried out the study of the implications of the Fritzsch-like texture 4 zero mass matrices. It may be noted that Fritzsch-like texture 4 zero mass matrices can be obtained by considering both M U and M D , with non zero D i (i = U, D) in Eq.…”

“…Their analysis has also given valuable clues about the phase structure of the mass matrices, in particular for the strong hierarchy case they conclude that only one of the two phase parameters plays a dominant role. Subsequently, attempts [14,22] have been made to update and broaden the scope of the analysis carried out by Xing and Zhang [13], in particular regarding the structural features of the mass matrices having implications for the value of parameter sin 2β.…”

“…The other issue is whether we can consider 'weakly' hierarchical mass matrices to reproduce 'strongly' hierarchical mixing angles. This issue has been explored in a detailed manner [14,22] and in the present work we reproduce some of the essential details regarding this. In this context, on the one hand, many authors [15]- [20] have shown that on using strong hierarchy of the elements of the mass matrices, texture 4 zero mass matrices appear to be incompatible with the recent value of sin 2β.…”

“…In this context, on the one hand, many authors [15]- [20] have shown that on using strong hierarchy of the elements of the mass matrices, texture 4 zero mass matrices appear to be incompatible with the recent value of sin 2β. While on the other hand, recently [14,22] extension of the parameter space of the elements of these matrices has been carried out to include the case of 'weak hierarchy' amongst them along with the usually considered 'strong hierarchy' case and thereby they have been shown to be compatible with the parameter sin 2β.…”