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Register a new userNeutrino Physics and Leptonic Weak Basis Invariants
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M. N. Rebelo
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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.
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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.
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.
We point out that leptonic weak-basis invariants are an important tool for the study of the properties of lepton flavour models. In particular, we show that appropriately chosen invariants can give a clear indication of whether a particular lepton flavour model favours normal or inverted hierarchy for neutrino masses and what is the octant of $theta_{23}$. These invariants can be evaluated in any conveniently chosen weak-basis and can also be expressed in terms of neutrino masses, charged lepton masses, mixing angles and CP violation phases.
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.
It is well recognized that looking for new physics at lower energy colliders is a tendency which is complementary to high energy machines such as LHC. Based on large database of BESIII, we may have a unique opportunity to do a good job. In this paper we calculate the branching ratios of semi-leptonic processes $D^+_s to K^+ e^-e^+$, $D^+_s to K^+ e^-mu^+$ and leptonic processes $D^0 to e^-e^+$, $D^0 to e^-mu^+$ in the frames of $U(1)$ model, 2HDM and unparticle separately. It is found that both the $U(1)$ and 2HDM may influence the semi-leptonic decay rates, but only the $U(1)$ offers substantial contributions to the pure leptonic decays and the resultant branching ratio of $D^0 to e^-mu^+$ can be as large as $10^{-7}sim10^{-8}$ which might be observed at the future super $tau$-charm factory.
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