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Register a new userPredictions on the second-class current decays $tau^{-}topi^{-}eta^{(prime)} u_{tau}$
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We analyze the second-class current decays $tau^{-}topi^{-}eta^{(prime)} u_{tau}$ in the framework of Chiral Perturbation Theory with resonances. Taking into account $pi^{0}$-$eta$-$eta^{prime}$ mixing, the $pi^{-}eta^{(prime)}$ vector form factor is extracted, in a model-independent way, using existing data on the $pi^{-}pi^{0}$ one. For the participant scalar form factor, we have considered different parameterizations ordered according to their increasing fulfillment of analyticity and unitarity constraints. We start with a Breit-Wigner parameterization dominated by the $a_{0}(980)$ scalar resonance and after we include its excited state, the $a_{0}(1450)$. We follow by an elastic dispersion relation representation through the Omn`{e}s integral. Then, we illustrate a method to derive a closed-form expression for the $pi^{-}eta$, $pi^{-}eta^{prime}$ (and $K^{-}K^{0}$) scalar form factors in a coupled-channels treatment. Finally, predictions for the branching ratios and spectra are discussed emphasizing the error analysis. An interesting result of this study is that both $tau^{-}topi^{-}eta^{(prime)} u_{tau}$ decay channels are promising for the soon discovery of second-class currents at Belle-II. We also predict the relevant observables for the partner $eta^{(prime)}_{ell 3}$ decays, which are extremely suppressed in the Standard Model.
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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.
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.
In this article, we have predicted the standard model (SM) values of the asymmetric and angular observables in $Bto D^{(ast)}tau u_{tau}$ decays, using the results of the new up-to-date analysis in $Bto D^{(*)}ell u_{ell}$. We have also revisited the SM prediction of the inclusive ratio $mathcal{R}_{X_c}$, and have given its values in different schemes of the charm quark mass. This is the first analysis which includes all the known corrections in the SM. In addition, we have analysed the $bto ctau u_tau$ decay modes in a model-independent framework of effective field theory beyond the standard model. Considering all the possible combinations of the effective operators in $b to c tau u_{tau}$ decays and using the Akaike Information Criterion, we find out the scenarios which can best explain the available data on these channels. In the selected scenarios, best-fit values and correlations of the new parameters are extracted. Using these results, predictions are made on various observables in the exclusive and inclusive semitaunic $b to c $ decays. The graphical correlations between these observables are shown, which are found to be useful in discriminating various new physics scenarios.
The cross sections and polarization components of the $tau$ leptons produced in the charged current induced quasielastic $ u_tau~(bar u_tau) - N$ scattering have been studied. The theoretical uncertainties arising due to the use of different vector form factors and the axial dipole mass in the axial vector form factor have been investigated. Due to the high mass of $tau$ lepton, the contributions from the term containing pseudoscalar and second class current form factors are non-negligible and contribute to the uncertainty in the cross section and polarization observables as these form factors are not well known. In view of the currently proposed experiments by DUNE, SHiP and DsTau collaborations to study the production of $tau$ lepton, an updated calculation of the cross sections and polarizations of tau leptons in the case of quasielastic production have been done and the numerical results have been presented along with a discussion of the theoretical uncertainties.
The rare $tau^- to eta^{(prime)} pi^- u_tau$ decays, which are suppressed by $G$-parity in the Standard Model (SM), can be sensitive to the effects of new interactions. We study the sensitivity of different observables of these decays in the framework of an effective field theory that includes the most general interactions between SM fields up to dimension six, assuming massless neutrinos. Owing to the strong suppression of the SM isospin breaking amplitudes, we find that the different observables would allow to set constraints on scalar interactions that are stronger than those coming from other low-energy observables.
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