Seeking Texture Zeros in the Quark Mass Matrix Sector of the Standard Model

Abstract

Here we show that the Weak Basis Transformation is an appropriate mathematical tool that can be used to find texture zeros in the quark mass matrix sector of the Standard Model. So, starting with the most general quark mass matrices and taking physical data into consideration, is possible to obtain more than three texture zeros by any weak basis transformation. Where the most general quark mass matrices considered in the model, were obtained through a special weak basis wherein the mass matrix $M_u$~(or $M_d$) has been taken to be diagonal and only the matrix $M_d$~(or $M_u$) is considered to be most general.