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Register a new userWeak Basis Transformations and Texture Zeros in the Leptonic Sector
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We investigate the physical meaning of some of the texture zeros which appear in most of the Ansatze on leptonic masses and their mixing. It is shown that starting from arbitrary lepton mass matrices and making suitable weak basis transformations one can obtain some of these sets of zeros, which therefore have no physical content. We then analyse four-zero texture Ansatze where the charged lepton and neutrino mass matrices have the same structure. The four texture zeros cannot be obtained simultaneously through weak basis transformations, so these Ansatze do have physical content. We show that they can be separated into four classes and study the physical implications of each class.
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In this talk, we present a recent investigation of the sufficient and necessary conditions for CP conservation in the leptonic sector with massive Majorana neutrinos in terms of CP-odd weak-basis invariants. The number of weak-basis invariants to guarantee CP conservation in the leptonic sector is clarified and a new set of invariants are advocated for the description of CP conservation, given the physical parameters in their experimentally allowed regions.
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 from zero textures appearing in the leptonic mass matrices. In this case an important question is, how can a flavour model corresponding to a set of texture zeros be recognised, when written in a different weak basis, where the zeros are not explicitly present. Another important application is the construction of invariants sensitive to the neutrino mass ordering and the $theta_{23}$ octant.
We investigate scaling ansatz with texture zeros within the framework of linear seesaw mechanism. In this variant of seesaw mechanism a simplified expression of effective neutrino mass matrix $m_ u$ containing two Dirac type matrices ($m_D$ and $m_{DS}$) and one Majorana type matrix ($m_{RS}$) is obtained by virtue of neglecting the global $U(1)_L$ symmetry breaking term in the mass term of the Lagrangian. Along with the charged lepton mass matrix, the matrix $m_{RS}$ too, is chosen in a diagonal basis whereas a scaling relation is incorporated in $m_D$ and $m_{DS}$ with different scale factors. Our goal in this work is to achieve a completely phenomenologically acceptable $m_ u$ generated by combinations of $m_D$ and $m_{DS}$ containing least number of independent parameters or maximum number of zeros. At the end of the numerical analysis it is found that number of zeros in any of the constituent Dirac type matrices ($m_D$ and $m_{DS}$) of $m_ u$ cannot be greater than six in order to meet the phenomenological requirements. The hierarchy obtained here is normal and also the values of the two parameters sum mass ($sum m_i$) and $|m_{ u_{ee}}|$ are below the present experimental lower limit.
The recent experimental developments require a more precise theoretical study of weak decays of heavy baryon $Lambda_b^0$. In this work, we provide an updated and systematic analysis of both the semi-leptonic and nonleptonic decays of $Lambda^0_b$ into baryons $Lambda^+_c$, $Lambda$, $p$, and $n$. The diquark approximation is adopted so that the methods developed in the $B$ meson system can be extended into the baryon system. The baryon-to-baryon transition form factors are calculated in the framework of a covariant light-front quark model. The form factors $f_3, ~g_3$ can be extracted and are found to be non-negligible. The semi-leptonic processes of $Lambda^0_bto Lambda^+_c(p)l^-bar u_l$ are calculated and the results are consistent with the experiment. We study the non-leptonic processes within the QCD factorization approach. The decay amplitudes are calculated at the next-to-leading order in strong coupling constant $alpha_s$. We calculate the non-leptonic decays of $Lambda^0_b$ into a baryon and a s-wave meson (pseudoscalar or vector) including 44 processes in total. The branching ratios and direct CP asymmetries are predicted. The numerical results are compared to the experimental data and those in the other theoretical approaches. Our results show validity of the diquark approximation and application of QCD factorization approach into the heavy baryon system.
We perform a systematic analysis of all possible texture zeros in general and symmetric quark mass matrices. Using the values of masses and mixing parameters at the electroweak scale, we identify for both cases the maximally restrictive viable textures. Furthermore, we investigate the predictive power of these textures by applying a numerical predictivity measure recently defined by us. With this measure we find no predictive textures among the viable general quark mass matrices, while in the case of symmetric quark mass matrices most of the 15 maximally restrictive textures are predictive with respect to one or more light quark masses.
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