Abstract
In this work, we proceed to study the CP asymmetry in the angular distributions of τ → KSπντ 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 non-zero CP asymmetry in the angular distributions, in the presence of complex couplings. Using the dispersive representations of the Kπ 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 Kπ invariant-mass bins as set by the Belle collaboration. Bounds on the effective couplings of the non-standard 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 τ−→ KSπ−ντ decay, with the numerical results given respectively by operatorname{Im}left[{hat{upepsilon}}_Sright] = −0.008 ± 0.027 and operatorname{Im}left[{hat{upepsilon}}_Tright] = 0.03 ± 0.12, at the renormalization scale μτ = 2 GeV in the overline{mathrm{MS}} scheme. Using the best-fit values, we also find that the distributions of the CP asymmetries can deviate significantly from the SM expectation in almost the whole Kπ invariant-mass region. Nevertheless, the current bounds on operatorname{Im}left[{hat{upepsilon}}_Sright] and operatorname{Im}left[{hat{upepsilon}}_Tright] 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. Assuming further that the non-standard scalar and tensor interactions originate from a weakly-coupled heavy new physics well above the electroweak scale, the SU(2)L invariance of the resulting SMEFT Lagrangian would indicate that very strong limits on operatorname{Im}left[{hat{upepsilon}}_Sright] and operatorname{Im}left[{hat{upepsilon}}_Tright] could also be obtained from the neutron electric dipole moment and the {D}^0-{overline{D}}^0 mixing. With the bounds from these processes taken into account, it is then found that, unless there exist extraordinary cancellations between the new physics contributions, neither the scalar nor the tensor interaction can produce any significant effects on the CP asymmetries (relative to the SM predictions) in the processes considered, especially under the “single coefficient dominance” assumption.
Highlights
The two CP -conjugated processes, there exists no direct CPV in these decays
The suppression of the relative phase between the Kπ vector and tensor form factors as well as the combined constraints from other relevant observables have already excluded such a possibility [34,35,36]. It has been shown in ref. [37] that, using a gauge-invariant dimension-eight tensor operator, one can account for the CP anomaly while evading the most stringent bound from the neutron electric dipole moment (EDM) and keeping at the same time the extraction of |Vus| from exclusive τ decays unaffected, such a scenario would induce a host of other issues, such as the breakdown of the power counting of the underlying effective field theory (EFT) as well as the constraints from the spectrum of τ − → KSπ−ντ decay itself and the semi-leptonic kaon decays [26]
We have performed a detailed study of the CP asymmetry in the angular distributions of τ → KSπντ decays within a general EFT framework including four-fermion operators up to dimension-six
Summary
Before presenting our numerical results, we firstly collect in table 1 all the input parameters used throughout this work; for any further details, the readers are referred to the references therein. The resulting limit on the CP -violating parameter Im(ηS) (which is equivalent to −Im[ˆS] of this work) at the 90% confidence level (C.L.) is in the range |Im(ηS)| < 0.026 or better, depending on the parametrization used to describe the hadronic form factors [30], and improves upon the previous CLEO limit [29] by about one order of magnitude This demonstrates the great potential of the CP -violating angular observables in probing the non-standard scalar interactions. As argued already, once the combined constraints from the branching ratios of τ − → KSπ−ντ , τ − → K−ηντ and τ − → K−ντ decays, as well as the decay spectrum of τ − → KSπ−ντ decay are taken into account [79], the impact of the real parts of the non-standard scalar and tensor couplings, Re[ˆS] and Re[ˆT ], on the CP asymmetry in the angular distributions of τ → KSπντ decays will be negligible. We will take the more stringent bounds on Re[ˆS] and Re[ˆT ] obtained in ref. [79], and are left with two NP parameters to be constrained, i.e., Im[ˆS] and Im[ˆT ], denoting the imaginary parts of the non-standard scalar and tensor couplings, respectively
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