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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 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
, 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
Anstze 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 ~(or ) has been
taken to be diagonal and only the matrix ~(or ) 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 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
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