We construct the CP-odd weak basis invariants from the neutrino mass matrix in a weak basis in which the charged lepton mass matrix is diagonal and find the necessary and sufficient conditions for CP conservation. We study the interrelationships between different CP-odd weak basis invariants to examine their implications for the Dirac and Majorana type CP violating phases for the phenomenologically allowed Frampton-Glashow-Marfatia texture zero structures of the neutrino mass matrix.
The phenomenon of time-reversal violating generation of static magnetic and electric fields is a basis of a new method for measurement of the electron EDM and T-odd P-odd constants of electron interaction with a nucleon beyond Standard Model
In this paper, we consider a three-zero texture with diagonal reflection symmetries in the SM. The three-zero texture has two less assumptions ($(M_{u})_{11} , (M_ν)_{11} \neq 0$) than the universal four-zero texture of mass matrices $(M_{f})_{11} = (M_{f})_{13,31} = 0$ for $f = u,d,ν, e$. The texture allows diagonal reflection symmetries to be almost exact and $d$\,-\,$e$ unification. They reproduce the CKM and MNS matrices with accuracies of $O(10^{-4})$ and $O(10^{-3})$. Some perturbative diagonalizations yield two relations with good accuracy for quark mass and mixing. Although this calcul…
In this paper, we derive the relationship between the weak basis invariants (WB) related to CP violation responsible for leptogenesis and CP violation relevant at low energy. We examine all the experimental viable cases of Frampton-Glashow and Yanagida (FGY) model, in order to construct the WB invariants in terms of left handed Majorana neutrino mass matrix elements, and thus finding the necessary and sufficient condition for CP conservation. Further for all the viable FGY texture zeros, we have shown the explicit dependence of WB invariants on Dirac type and Majorana type CP violating phases.…
In the seesaw framework, in the basis of $M^{}_{\rm R}$ being diagonal, we explore the simplified textures of $M^{}_{\rm D}$ that can naturally yield the trimaximal neutrino mixings and their consequences for the neutrino parameters and leptogenesis. We first formulate the generic textures of $M^{}_{\rm D}$ that can naturally yield the trimaximal mixings and then examine if their parameters can be further reduced. Our analysis is restricted to the simple but instructive scenario that there is only one phase parameter $ϕ$ responsible for both the CP violating effects at low energies and leptoge…
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 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…
Reply to "Comment on "Texture Zeros and WB Transformations in the Quark Sector of the Standard Model"
我们回应S的评论。Sharma等人[Phys. Rev. D 91，038301（2015）]在我最近的论文中，Y. Giraldo [Phys. Rev. D 86，093021（2012）]。在他们的评论中，他们开始讨论我提出的一类特殊的五零纹理非弗里奇夸克质量矩阵，并质疑其有效性。然后，他们对用于对角化夸克质量矩阵的酉矩阵中包含的相位提出了质疑，并声称由此得到的CP破坏参数$ε_k$与实验值不一致。由于这些评论，最后，他们建议在分析弱基变换对纹理的影响时要小心。他们还讨论了其他一些次要问题。在下文中，我将证明所提到的五个零纹理的非Fritzsch类夸克质量矩阵是完全有效的，并产生所有涉及的物理量，包括CP破坏参数$ε_k$，这是需要在用于对角化夸克质量矩阵的酉矩阵中包含相位，以便将CKM矩阵置于标准形式。这些相位可以旋转，因此它们没有任何物理意义。最后，弱基变换的相关性是赞赏：这是{ \it完成}，并有利于计算，特别是纹理零。
The scotogenic model is well known for accommodating small neutrino mass and dark matter. Here, we have realized the scotogenic model with the help of discrete flavor symmetry $A_{4}\otimes Z_{4}$. We have obtained three one zero textures of Yukawa coupling matrices from the model and have studied its impact on neutrino phenomenology and related aspects of cosmology. On the basis of $μ-τ$ symmetry, we have further discarded two structures of one zero texture Yukawa coupling matrix. We further analyze if the effective mass of active neutrinos obtained by the virtue of the Yukawa coupling matrix…
We introduce an unconventional interpretation of the fermion mass matrix elements. As the full rotational freedom of the gauge-kinetic terms renders a set of infinite bases called weak bases, basis-dependent structures as mass matrices are unphysical. Matrix invariants, on the other hand, provide a set of basis-independent objects which are of more relevance. We employ one of these invariants to give a new parametrization of the mass matrices. By virtue of it, one gains control over its implicit implications on several mass matrix structures. The key element is the trace invariant which resemb…
In this talk we present a powerful tool applied to the study of Leptonic Physics. This tool is based on the construction of Weak Basis invariant relations associated to different properties of leptonic models. The rationale behind these constructions is the fact that fermion mass matrices related through weak basis transformations look different but lead to the same physics. Such invariants can be built, for instance, with the aim to test leptonic models for different types of CP violation. These invariants are also relevant beyond such tests and have been applied to the study of implications …
We classify all possible texture zeros in light neutrino mass matrix in diagonal charged lepton basis by considering Dirac nature of light neutrinos. For Hermitian nature of neutrino mass matrix, the number of possible texture zeros remain same as Majorana texture zeros, but with less free parameters due to the absence of additional Majorana CP phases. Relaxing the Hermitian nature of neutrino mass matrix lead to many more possibilities and freedom due to additional CP phases, mixing angles not constrained by neutrino data. While we find that none of the texture zeros in Hermitian case are all…
In this work we carry out an exhaustive study to find quark mass matrices in the Standard Model~(SM), with the maximum number of texture zeros consistent with the experimental data. We found four viable configurations of five texture zeros that adjust the quark masses, the mixing angles and the CP violation phase, with deviations below $1σ$ level respect to the current SM best fit values. One of the most important aspects of this work is an economic procedure to find the texture zeros: we resort to the weak basis transformation method, which, as we will show, exhaustively search every possible…
In the light of latest neutrino oscillation data, we have investigated the one zero Majorana neutrino mass matrix $M_ν$ with zero sum condition of mass eigen values in the flavor basis, where charged lepton mass matrix is diagonal. Among the six possible one-zero cases, it is found that only five can survive the current experimental data, while case with (1, 1) vanishing element of $M_ν$ is ruled out, if zero trace condition is imposed at 3$σ$ confidence level (CL). Numerical and some approximate analytical results are presented.
