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Register a new userCombined analysis of the decays $tau^{-}to K_{S}pi^{-} u_{tau}$ and $tau^{-}to K^{-}eta u_{tau}$
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Sergi Gonzalez-Solis
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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.
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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.
We report a feasibility study of $CP$ violation of $tau^{-}rightarrow K_{S}pi^{-} u_{tau}$ decay at a Super Tau Charm Facility~(STCF).With an expected luminosity of 1~ab$^{-1}$ collected by STCF per year at a center-of-mass energy of 4.26 GeV, the statistical sensitivity for the $CP$ violation is determined to be of order $9.7times10^{-4}$ by measuring the decay-rate difference between $tau^{+}rightarrow K_{S}pi^{+}bar{ u}_{tau}$ and $tau^{-}rightarrow K_{S}pi^{-} u_{tau}$. The analysis is performed using a reliable fast simulation software package, which can describe the detector responses properly and vary the responses flexibly for further optimization. Moreover, the energy-dependent efficiencies for reconstructing $tau^{-}rightarrow K_{S}pi^{-} u_{tau}$ are presented and the expected $CP$ sensitivity is proportional to $1/sqrt{mathcal{L}}$ in the energy region from 4.0 to 5.0 GeV. The sensitivity of $CP$ violation is of order $3.1times10^{-4}$ with 10~ab$^{-1}$ integrated luminosity, which is equivalent to ten years data taking in this energy region at STCF.
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.
We present the first measurements of branching fractions of rare tau-lepton decays, $tau^- rightarrow pi^- u_{tau} ell^+ ell^-$ ($ell = e$ or $mu$), using a data sample corresponding to 562 fb$^{-1}$ collected at a center-of-mass energy of 10.58 GeV with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. The $tau^- rightarrow pi^- u_tau e^+ e^-$ decay is observed for the first time with 7.0$sigma$ significance. The partial branching fraction determined by the structure-dependent mechanisms mediated by either a vector or an axial-vector current for the mass region $M_{pi e e}>1.05$ GeV/$c^2$ is measured to be $mathcal{B}(tau^-rightarrow pi^- u_tau e^+ e^-)[M_{pi^- e^+ e^-}>1.05~{rm GeV}/c^2] = (5.90 pm 0.53 pm 0.85 pm 0.11) times 10^{-6}$, where the first uncertainty is statistical, the second is systematic, and the third is due to the model dependence. In the full phase space, due to the different detection efficiencies for the structure-dependent mechanisms mediated by axial-vector and vector currents, the branching fraction varies from $mathcal{B}_{A}(tau^-rightarrow pi^- u_tau e^+ e^-) = (1.46 pm 0.13 pm 0.21) times 10^{-5}$ to $mathcal{B}_{V}(tau^-rightarrow pi^- u_tau e^+ e^-) = (3.01 pm 0.27 pm 0.43) times 10^{-5}$, respectively. An upper limit is set on the branching fraction of the $tau^- rightarrow pi^- u_tau mu^+ mu^-$ decay, $mathcal{B}(tau^-rightarrow pi^- u_tau mu^+ mu^-) < 1.14 times 10^{-5}$, at the 90% confidence level.
A general analysis of possible violation of CP in processes like $tau to Kpi u$, for unpolarized $tau$ is presented. In this paper, we derive the new contributions to the effective Hamiltonian governs $vertDelta S vert=1$ semileptonic tau decays in the framework of two Higgs doublet model with generic Yukawa structure and Leptoquarks models. Within these models, we list all operators, in the effective Hamiltonian and provide analytical expression for their corresponding Wilson coefficients. Moreover, we analyze the role of the different contributions, originating from the scalar, vecor and tensor hadronic currents, in generating direct CP asymmetry in the decay rate of $tau^-to K^-pi^0 u_tau$. We show that non vanishing direct CP asymmetry in the decay rate of $tau^-to K^-pi^0 u_tau$ can be generated due to the presence of both, the weak phase in the Wilson coefficient corresponding to the tensor operator and the strong phase difference resulting from the interference between the form factors expressing the matrix elements of the vector and tensor hadronic currents. After taking into account all relevant constraints, we find that the generated direct CP asymmetry is of order $10^{-8}$ which is several orders of magnitude larger than the standard model prediction. We show also that, in two Higgs doublet model with generic Yukawa structure , direct local or non integrated CP violation can be as large as $0.3$ % not far from experimental possibilities. This kind of asymmetry can be generated due to the interference between vector and scalar contributions with different weak phases which is not the case in the SM.
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