Implications of CP asymmetry parameter sin2beta on structural features of texture specific mass matrices

Abstract

In the context of Fritzsch-like texture 4 zero Hermitian quark mass matrices, we have attempted to find an 'exact' formula for sin 2β wherein the dependence of β 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 sin 2β and other CKM parameters, we find interesting conclusions regarding the structural features of the mass matrices.

Quark flavor mixings from hierarchical mass matrices

“…( 2) and the parallel four-zero texture in Eq. ( 3) is that a hierarchical structure is not allowed in the latter case [39,40,53,54]. Even more, it has recently been found in Ref.…”

“…where q = u or d denotes the up-type or down-type quark mass matrix, and a pair of off-diagonal texture zeros in the Hermitian or symmetric matrix are usually counted as one zero. As a consequence of texture zeros [32][33][34][35][36][37][38][39][40][41][42], a few simple but instructive relations among flavor mixing angles and quark mass ratios can be estab-lished [34,36,[43][44][45][46][47][48][49] and tested in experiments. Unfortunately, the Fritzsch ansatz failed to reconcile a large top-quark mass with the observed value of |V cb | [50,51].…”

Pieces of the flavour puzzle

“…All possible combinations of hermitian 6-zero and 5-zero textures are ruled out by now 2 , because they cannot reproduce |V cb |, with the only exception of y f in (50) with D u = 0 and D d = 0, which is marginally compatible with present data [82]. The 4-zero texture in (50) with both D u and D d non vanishing is still allowed, provided the hierarchy in the 23 block is mild [83,84]. In particular |B f /C f | should be O(0.1).…”