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

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

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

Cinco ceros de textura de tipo no Fritzsch para las matrices de masa de los quarks en el Modelo Estándar

Vamos a considerar un modelo con cinco ceros de textura que no es del tipo Fritzsch para las matrices de masa de los quarks, que es completamente válido y genera todas las cantidades físicas de interés: que incluye las masas de los quarks, la cantidad invariante de Jarlskog y los ángulos internos del triángulo unitario de Cabibbo-Kobayashi-Maskawa. Para lograr esto, debemos incluir fases no físicas en las matrices unitarias que diagonalizan las matrices de masa de los quarks, a fin de llevar la matriz de Cabibbo-Kobayashi-Maskawa a su forma estándar. Así que el modelo tiene nueve parámetros para reproducir diez cantidades físicas, lo que implica relaciones entre las masas de los quarks y sus mezclas. Este trabajo tiene varios resultados importantes: a) Primero decir que los ceros de textura buscan reducir el número de parámetros libres presentes en el Modelo Estándar, que para nuestro caso, con sólo nueve parámetros se logra reproducir cantidades físicas de interés, lo implica predicciones, principalmente entre los ángulos de mezcla CKM y las masas de los quarks, entre ellas, verificamos la relación de Gatto-Sartori-Tonin. b) Mostramos que cinco (5) ceros de textura es el máximo número de ceros posibles en las matrices de masa de los quarks. c) Los patrones de distribución de los posibles ceros de textura también está limitado: dos ceros en la matriz de masa up y tres en la matriz de masa down. d) Encontramos una importante fuente de violación CP puesto que el ángulo de fase es cercano a pi/2

Ceros de Textura en el Sector de Quarks del Modelo Estándar

Si bien, el sector gauge del Modelo Estándar (ME) con la simetrı́a SU(3)C⊗SU(2)L⊗U(1)Y es muy exitoso, el sector de Yukawa del ME sigue siendo aún poco conocido. El origen de las masas de los fermiones, los ángulos de mezcla y la violación CP permanecen como problemas abiertos de la fı́sica de partı́culas. Ha habido una gran cantidad de estudios sobre las simetrı́as fundamentales posibles en las matrices de acoplamiento de Yukawa del ME. Por consiguiente, en ausencia de una teorı́a más fundamental de las interacciones, un enfoque independiente del modelo feno- menológico para buscar posibles texturas o simetrı́as en las matrices de masa fermiónicas sigue jugando todavı́a un papel importante

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

Scalar Sector of 331 Models Without Exotic Electric Charges

In this work, we study the minimal set of Higgs scalars, for models based on the local gauge group SU(3)c⊗SU(3)L⊗U(1)X which do not contain particles with exotic electric charges. We show that only two Higgs SU(3)L triplets are needed in order to properly break the symmetry. The exact tree-level scalar mass matrices resulting from symmetry breaking are calculated at the minimum of the most general scalar potential, and the gauge bosons are obtained, together with their coupling to the physical scalar fields. We show how the scalar sector introduced is enough to produce masses for fermions in a particular model which is an E 6 subgroup. By using experimental results we constraint the scale of new physics to be above 1.3 TeV. Also, a detailed study of the criteria for stability of the scalar potential and the proper electroweak symmetry breaking pattern in the economical 331 model, is presented. For the analysis we use, and improve, a method previously developed to study the scalar potential in the two-Higgs-doublet extension of the Standard Model (SM). A new theorem 2related to the stability of the potential is stated. As a consequence of this study, the consistency of the economical 331 model emerges. Additionally, we concentrate in a scalar sector with three Higgs scalar triplets, with a potential that does not include the cubic term, due to the presence of a discrete symmetry. Our main result is to show the consistency of those 331 models without exotic electric charges

Stability and Symmetry Breaking in the Two-Higgs-Doublet Model

A method is presented for the analysis of the scalar potential in the general Two-Higgs- Doublet Model. This allows us to give the conditions for the stability of the potential and for electroweak symmetry breaking in this model in a very concise way. These results are then applied to different Higgs potentials in the literature, specifically the Two-Higgs-Doublet potential proposed by Gunion et al. The known results for this model follow easily as special cases from the general results