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We derive the corrections induced by the W-boson propagator to the differential rates of the leptonic decay of a polarized muon and tau lepton. Results are presented both for decays inclusive of inner bremsstrahlung as well as for radiative ones, when a photon emitted in the decay process is measured. The numerical effect of these corrections is discussed. The definition of the Fermi constant is briefly reviewed.
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The branching fractions of radiative leptonic $tau$ decays $(tau to l u bar{ u} gamma$, $l=e,mu)$ were recently measured by the Babar collaboration with a relative error of about 3%. The measurement of the branching ratio $mathcal{B} (tau to e bar{ u} u gamma)$, for a minimum photon energy of 10 MeV in the $tau$ rest frame, differs from our recent SM prediction by 3.5 standard deviations, whereas our result agrees with Babars value for $mathcal{B} (tau to mu bar{ u} u gamma)$. Our predictions also agree with the measurement of $mathcal{B} (mu to e bar{ u} u gamma)$ by the MEG collaboration. We also report on a recent proposal to test the $tau$ dipole moments via precise measurements of radiative leptonic $tau$ decays at high-luminosity $B$ factories.
The potential of performing a combined analysis of the strangeness-changing decays $tau^{-}to K_{S}pi^{-} u_{tau}$ and $tau^{-}to K^{-}eta u_{tau}$ for unveiling the $K^{*}(1410)$ resonance pole parameters is illustrated. Our study is carried out within the framework of Chiral Perturbation Theory, including resonances as explicit degrees of freedom. Resummation of final state interactions are considered through a dispersive parameterization of the required form factors. A considerable improvement in the determination of the pole position with mass $M_{K^{*}(1410)}=1304pm17$ MeV and width $Gamma_{K^{*}(1410)}=171pm62$ MeV is obtained.
We study the effects induced by excited leptons on the leptonic tau decay at one loop level. Using a general effective lagrangian approach to describe the couplings of the excited leptons, we compute their contributions to the leptonic decays and use the current experimental values of the branching ratios to put limits on the mass of excited states and the substructure scale.
In a combined study of the decay spectra of $tau^-to K_Spi^- u_tau$ and $tau^-to K^-eta u_tau$ decays within a dispersive representation of the required form factors, we illustrate how the $K^*(1410)$ resonance parameters, defined through the pole position in the complex plane, can be extracted with improved precision as compared to previous studies. While we obtain a substantial improvement in the mass, the uncertainty in the width is only slightly reduced, with the findings $M_{K^{*prime}}=1304 pm 17,$MeV and $Gamma_{K^{*prime}} = 171 pm 62,$MeV. Further constraints on the width could result from updated analyses of the $Kpi$ and/or $Keta$ spectra using the full Belle-I data sample. Prospects for Belle-II are also discussed. As the $K^-pi^0$ vector form factor enters the description of the decay $tau^-to K^-eta u_tau$, we are in a position to investigate isospin violations in its parameters like the form factor slopes. In this respect also making available the spectrum of the transition $tau^-to K^-pi^0 u_tau$ would be extremely useful, as it would allow to study those isospin violations with much higher precision.
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.
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