Reply to "Comment on "Texture Zeros and WB Transformations in the Quark Sector of the Standard Model"

We respond to the comments of S. Sharma et al. [Phys. Rev. D 91, 038301 (2015)] on my recent paper, Y. Giraldo [Phys. Rev. D 86, 093021 (2012)]. In their comments, they begin discussing a particular class of five-zero texture non-Fritzsch-like quark mass matrix, which was proposed by me, and questioning its validity. Then, they put in doubt the phases included in the unitary matrices used for diagonalizing the quark mass matrices, from which they claim that the CP violating parameter $\epsilon_k$ obtained does not agree with the experimental value. Because of these comments, finally, they recommend being careful while analyzing the implications of Weak Basis transformations on textures. Other minor points are also discussed by them. In the following, I will show that the mentioned five-zero texture non-Fritzsch-like quark mass matrices is completely valid and generates all the physical quantities involved, including the CP violating parameter $\epsilon_k$, for which is required the inclusion of phases in the unitary matrices used for diagonalizing the quark mass matrices in order to put the CKM matrix in standard form. These phases can be rotated away so they do not have any physical meaning. Finally, the relevance of the weak basis transformation is appreciated: which is {\it complete} and facilitates calculations, especially of textures zeros

Texture Zeros and WB Transformations in the Quark Sector of the Standard Model

Stimulated by the recent attention given to the texture zeros found in the quark mass matrices sector of the Standard Model, an analytical method for identifying (or to exclude) texture zeros models will be implemented here, starting from arbitrary quark mass matrices and making a suitable weak basis transformation, we are be able to find equivalent quark mass matrix. It is shown that the number of non-equivalent quark mass matrix representations is finite. We give exact numerical results for parallel and non-parallel four-texture zeros models. We find that some five-texture zeros Ans$\ddot{\textrm{a}}$tze are in agreement with all present experimental data. And we confirm definitely that six-texture zeros of Hermitian quark mass matrices are not viable models anymore.Comment: 19 pages, version 3 corrects for typos, text minor updated, improvements in the text, numerical physical data update

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

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.Comment: 3 pages. Contribution to the proceedings of the 10th Simposio Latinoamericano de F\'isica de Altas Energ\'ias (X SILAFAE) - Ruta N, Medell\'in, Colombia, November 24-28 2014. arXiv admin note: text overlap with arXiv:1502.0726

Five-Zero Texture non-Fritzsch like Quark Mass Matrices in the Standard Model

We will consider a five-zero texture non-Fritzsch like quark mass matrices that is completely valid and generates all the physical quantities involved, including the quark masses, the Jarlskog invariant quantity and the inner angles of the Cabibbo-Kobayashi-Maskawa unitarity triangle, and explaining the charge parity violation phenomenon at 1$\sigma$ confidence level. To achieve this, non-physical phases must be included in the unitary matrices used to diagonalize the quark mass matrices, in order to put the Cabibbo-Kobayashi-Maskawa matrix in standard form. Besides, these phases can be rotated away so they do not have any physical meaning. Thus, the model has a total of nine parameters to reproduce ten physical quantities, which implies physical relationships between the quark masses and/or mixings.Comment: 9 page