Texture zeros for the Standard Model quark mass matrices

Abstract

A way of counting free parameters in the quark mass matrices of the standard model, including the constraints coming from weak basis transformations, is presented; this allow to understand the exact physical meaning of the parallel and non-parallel texture zeros which appear in some "ansätz" of the 3 × 3 quark mass matrices, including the CP violation phenomena in the analysis, it is shown why the six texture zeros are ruled out. Finally, a five texture zeros "ansätze"which properly copes with all experimental constrains, including the angles of the unitary triangle, is presented.

Five texture zeros andCPviolation for the standard model quark mass matrices

“…This pattern was studied previously in Ref. [18]. The complex Hermitian quark mass matrices for this pattern can be written as:…”

“…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").…”

Model of flavor with quaternion symmetry

“…Interesting alternatives do exist. See, for example, the recent work in [31] where it is shown that having M u similar to Eq. (B1) and an M d given by…”

Exploring the predictability of symmetric texture zeros in quark mass matrices

“…In particular, it was observed [37][38][39][40] that all texture six zero hierarchical quark mass matrices were ruled out at the level of 3σ, which is a settled and uncontested result. Some predictive texture five zero structures were discussed in [13] which were subsequently ruled out in [38,41,42] on hierarchy and sin2β considerations.…”