Seeking Texture Zeros in the Quark Mass Matrix Sector of the Standard Model
Yithsbey Giraldo
备注：
3 pages. Contribution to the proceedings of the 10th Simposio Latinoamericano de Física de Altas Energías (X SILAFAE) - Ruta N, Medellín, Colombia, November 24-28 2014. arXiv admin note: text overlap with arXiv:1502.07260
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.
We consider a modification of the Fukuyama-Nishiura texture and compare it to the precision quark flavour data, finding that it fits the data very well but at the cost of accidental cancelations between parameters. We then propose different viable textures for quarks, where only the Cabibbo mixing arises from the down sector, and extend to the charged leptons while constructing a complementary neutrino structure that leads to viable lepton masses and mixing.
In this paper we investigate the parallel texture structures with cofactor zeros in the charged lepton and neutrino sectors. The textures can not be obtained from arbitrary leptonic matrices by making weak basis transformations, which therefore have physical meaning. The 15 parallel textures are grouped as 4 classes where each class has the same physical implications. It is founded that one of them is not phenomenological viable and another is equivalent to the texture zero structures extensively explored in previous literature. Thus we focus on the other two classes of parallel texture struct…
Recently, using specific Weak Basis transformations, Y. Giraldo [Phys. Rev. D 86, 093021 (2012)] has constructed some texture 5 and 4 zero quark mass matrices and examined their compatibility with the quark mixing data. In this comment, we have re-analyzed these to bring forth certain important issues regarding their viability which need to be taken note of.
We investigate the texture structures of lepton mass matrices with four (five) non-zero elements in the charged lepton mass matrix and three (four) vanishing cofactors in the neutrino mass matrix. Using weak basis transformations, all possible textures for three and four vanishing cofactors in $M_ν$ are grouped into 7 classes and predictions for the unknown parameters such as the Dirac CP violating phase and the effective Majorana mass for the phenomenologically allowed textures have been obtained. We, also, illustrate how such texture structures can be realized using discrete Abelian flavor s…
In the quark sector, Jarlskog rephasing invariant parameter $J_{CP}$ has important implications for the CP violation as well as phase structure of the quark mass matrices. In fact all CP violating effects in this sector are proportional to the magnitude of the imaginary part of $J_{CP}$ . With the observation of non-zero and large "reactor mixing angle", it is widely believed that CP might be violated in the leptonic sector. In this context, we have examined in detail the relationship of CP odd invariants for texture specific mass matrices. In particular, we have calculated the predicted range…
In the Standard Model, we obtain a non-Fritzsch like configuration with five texture zeros for the quark mass matrices. This matrix generates the quark masses, the inner angles of the CKM unitary triangle, and the CP-violating phase in the quark sector. This work can be applied to the PMNS matrix in the lepton sector, by assuming Dirac masses for the neutrinos, where non-trivial predictions for the neutrino masses and mixing angles are expected.
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 $ε_k$ obtained does not agree with the experimental value. Because of these comments, finally, they recommend b…
In the quark sector, Jarlskog rephasing invariant $\rm{J_{CP}}$ has important implications for the CP violation as well as phase structure of the quark mass matrices. In fact all CP violating effects in this sector are proportional to the magnitude of the imaginary part of $\rm{J_{CP}}$. With the observation of non-zero and relatively large reactor mixing angle $θ_{13}$, it is widely believed that CP might be violated in the lepton sector. The recent global best fits of neutrino oscillation indicates the preference of CP violation over CP conservation at relatively large confidence level. Thes…
We make a scalar extension of the B-L gauge model where the ${\bf S}_{3}$ non-abelian discrete group drives mainly the Yukawa sector. Motived by the large and small hierarchies among the quark and active neutrino masses respectively, the quark and lepton families are not treated on the same footing under the assignment of the discrete group. As a consequence, the Nearest Neighbor Interactions (NNI) textures appear in the quark sector, leading to the CKM mixing matrix, whereas in the lepton sector, a soft breaking of the $μ\leftrightarrow τ$ symmetry in the effective neutrino mass that comes fr…
In this work, we have assumed special structures for the charged and neutral mass matrices in the lepton sector, inspired by structures for the up and down quark mass matrices that result by assuming a certain number of symmetrical zeros in their entries named texture zeros. A prediction of the lepton mixing matrix results from the rotation matrices that diagonalize the mass matrices in the neutral and charged lepton sectors. The use of texture zeros reduces the number of spurious parameters to the minimal ones needed to explain observations i.e. charged lepton masses and neutrino oscillation …
In this letter we analyse, in the context of the general 2-Higgs Doublet Model, the structure of the Yukawa matrices, $\widetilde{ \bf Y}_{ _{1,2} }^{q}$, by assuming a four-zero texture ansatz for their definition. In this framework, we obtain compact expressions for $\widetilde{ \bf Y}_{ _{1,2} }^{q}$, which are reduced to the Cheng and Sher ansatz with the difference that they are obtained naturally as a direct consequence of the invariants of the fermion mass matrices. Furthermore, in order to avoid large flavour violating effects coming from charged Higgs exchange, we consider the main fl…
One- and two-zero textures for the flavor neutrino mass matrix have been successful in explaining mixing in the neutrino sector. Conservatively, six cases of one-zero textures and seven cases of two-zero textures are compatible with observations. We show that one case may be the most natural in the one- and two-zero textures schemes if tiny neutrino masses are generated by the type-II seesaw mechanism in triplet Higgs models.
We look for all weak bases that lead to texture zeroes in the quark mass matrices and contain a minimal number of parameters in the framework of the standard model. Since there are ten physical observables, namely, six nonvanishing quark masses, three mixing angles and one CP phase, the maximum number of texture zeroes in both quark sectors is altogether nine. The nine zero entries can only be distributed between the up- and down-quark sectors in matrix pairs with six and three texture zeroes or five and four texture zeroes. In the weak basis where a quark mass matrix is nonsingular and has si…
The $μτ$-reflection symmetric neutrino mass matrix can accommodate all known neutrino mixing angles, with maximal atmospheric angle fixed, and predicts all the unknown CP phases of the lepton sector but is unable to predict the absolute neutrino mass scale. Here we present a highly predictive scenario where $μτ$-reflection is combined with a discrete abelian symmetry to enforce a texture-zero in the mass matrix of the heavy right-handed neutrinos that generate the light neutrino masses. Such a restriction reduces the free parameters of the low energy theory to zero and the absolute neutrino ma…
The implementation of maximally restrictive texture zeros in the leptonic sector is investigated in the context of two-Higgs-doublet models with Majorana neutrinos. After analyzing all maximally restrictive pairs of leptonic mass matrices with zero entries, we conclude that there are only four texture combinations that are compatible with observations at 3 sigma confidence level and can be implemented through Abelian symmetries in a two-Higgs-doublet model. The compatibility of these textures with current constraints on lepton-flavor-violating processes is also studied. The ultraviolet complet…
We study a model of neutrino and dark matter within the framework of a minimal extended seesaw. This model is based on $A_4$ flavour symmetry along with the discrete $Z_3\times Z_4$ symmetry to stabilize the dark matter and construct desired mass matrices for neutrino mass. Five-zero textures are imposed in the final $4\times4$ active-sterile mass matrix, which significantly reduces free parameter in the model. Three right-handed neutrinos were considered, two of them have nearly degenerate masses which help us to achieve baryogenesis via resonant leptogenesis. A singlet fermion (sterile neutr…
Within the low scale resonant leptogenesis scenario, the cosmological CP asymmetry may arise by radiative corrections through the charged lepton Yukawa couplings. While in some cases, as one expects, decisive role is played by the $λ_{τ}$ coupling, we show that in specific neutrino textures only by inclusion of the $λ_{μ}$ the cosmological CP violation is generated at 1-loop level. With the purpose to relate the cosmological CP violation to the leptonic CP phase $δ$, we consider an extension of MSSM with two right handed neutrinos (RHN), which are degenerate in mass at high scales. Together wi…
In this work we revisit the zero textures in low energy Majorana neutrino mass matrix when the active neutrino sector is extended by a light sterile neutrino in the eV scale i.e., the 3+1 scheme. In 3+1 scenario, the low energy neutrino mass matrix ($m_ν$) has ten independent elements. Thus in principle one can have minimum one-zero texture to maximum ten-zero texture. We summarize the previous results of one, two, three and four-zero textures which already exist in the literature and present our new results on five-zero textures. In our analysis we find that among six possible five-zero textu…
We study the predictions for CP phases and absolute neutrino mass scale for broad classes of models with a U(2) flavor symmetry. For this purpose we consider the same special textures in neutrino and charged lepton mass matrices that are succesful in the quark sector. While in the neutrino sector the U(2) structure enforces two texture zeros, the contribution of the charged lepton sector to the PMNS matrix can be parametrized by two rotation angles. Restricting to the cases where at least one of these angles is small, we obtain three representative scenarios. In all scenarios we obtain a narro…
We investigate neutrino mass matrix phenomenology involving scaling ansatz and texture zeros adhering inverse seesaw mechanism. It is seen that four is the maximum number of zeros in $m_D$ and $μ$ to obtain viable phenomenology. Depending upon the generic nature of the effective neutrino mass matrices we classify all the emerged matrices in four categories. One of them is ruled out phenomenologically due to inappropriate value of reactor mixing angle after breaking of the scaling ansatz. The mass ordering is inverted in all cases. One of the distinguishable feature of all these categories is t…
Within the framework of inverse seesaw mechanism we investigate neutrino mass matrices invariant under cyclic symmetry ($Z_3$) with maximal zero texture (6 zero textures). We explore two different approaches to obtain the cyclic symmetry invariant form of the constituent matrices. In the first one we consider explicit cyclic symmetry in the neutrino sector of the Lagrangian which dictates the emerged effective neutrino mass matrix ($m_ν$) to be symmetry invariant and hence leads to a degeneracy in masses. We then consider explicit breaking of the symmetry through a dimensionless parameter $ε^{…
