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Register a new userEffective-field theory analysis of the $tau^- to eta^{(prime)} pi^- u_tau$ decays
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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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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 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.
Based on a sample of $1.31 times 10^9$ $J/psi$ events collected with the BESIII detector, an amplitude analysis of the isospin-violating decays $eta^prime rightarrow pi^+pi^-pi^0$ and $eta^prime rightarrow pi^0pi^0pi^0$ is performed. A significant $P$-wave contribution from $eta^prime rightarrow rho^{pm} pi^{mp}$ is observed for the first time in $eta^prime rightarrow pi^+pi^-pi^0$. The branching fraction is determined to be ${mathcal B}(eta^prime rightarrow rho^{pm}pi^{mp})=(7.44pm0.60pm1.26pm1.84)times 10^{-4}$, where the first uncertainty is statistical, the second systematic, and the third model dependent. In addition to the nonresonant $S$-wave component, there is a significant $sigma$ meson component. The branching fractions of the combined $S$-wave components are determined to be ${mathcal B}(eta^prime rightarrow pi^+pi^-pi^0)_S=(37.63pm0.77pm2.22pm4.48)times 10^{-4}$ and ${mathcal B}(eta^prime rightarrow pi^0pi^0pi^0)=(35.22pm0.82pm2.54)times 10^{-4}$, respectively. The latter one is consistent with previous BESIII measurements.
In this work, we proceed to study the $CP$ asymmetry in the angular distributions of $tauto K_Spi u_tau$ decays within a general effective field theory framework including four-fermion operators up to dimension-six. It is found that, besides the commonly considered scalar-vector interference, the tensor-scalar interference can also produce a nonzero $CP$ asymmetry in the angular distributions, in the presence of complex couplings. Using the dispersive representations of the $Kpi$ form factors as inputs, and taking into account the detector efficiencies of the Belle measurement, we firstly update our previous SM predictions for the $CP$ asymmetries in the same four $Kpi$ invariant-mass bins as set by the Belle collaboration. Bounds on the effective couplings of the nonstandard scalar and tensor interactions are then obtained under the combined constraints from the $CP$ asymmetries measured in the four bins and the branching ratio of $tau^-to K_Spi^- u_tau$ decay, with the numerical results given respectively by $mathrm{Im}[hat{epsilon}_S]=-0.008pm0.027$ and $mathrm{Im}[hat{epsilon}_T]=0.03pm0.12$, at the renormalization scale $mu=2~mathrm{GeV}$ in the $mathrm{overline{MS}}$ scheme. Using these best-fit values, we also find that the distributions of the $CP$ asymmetries can deviate significantly from the SM prediction in almost the whole $Kpi$ invariant-mass regions. The current bounds are still plagued by large experimental uncertainties, but will be improved with more precise measurements from the Belle II experiment as well as the proposed Tera-Z and STCF facilities.
A search for the $C!P$-violating strong decays $eta to pi^+pi^-$ and $eta^prime(958) to pi^+pi^-$ has been performed using approximately $2.5 times 10^{7}$ events of each of the decays $D^+ to pi^+pi^+pi^-$ and $D_s^+ to pi^+pi^+pi^-$, recorded by the LHCb experiment. The data set corresponds to an integrated luminosity of 3.0 fb$^{-1}$ of $pp$ collision data recorded during LHC Run 1 and 0.3 fb$^{-1}$ recorded in Run 2. No evidence is seen for $D^+_{(s)} to pi^+ eta^{(prime)}$ with $eta^{(prime)} to pi^+pi^-$, and upper limits at 90% confidence level are set on the branching fractions, $mathcal{B}(eta to pi^+pi^-) < 1.6 times 10^{-5}$ and $mathcal{B}(eta^prime to pi^+pi^-) < 1.8 times 10^{-5}$. The limit for the $eta$ decay is comparable with the existing one, while that for the $eta^prime$ is a factor of three smaller than the previous limit.
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