No-Go Theorem for Nonstandard Explanations of the $\tau \to K_S\pi {\nu }_{\tau }$ $CP$ Asymmetry

The $CP$ asymmetry in $\tau \to K_S\pi {\nu }_{\tau }$, as measured by the BABAR collaboration, differs from the standard model prediction by $2.8\sigma$. Most nonstandard interactions do not allow for the required strong phase needed to produce a nonvanishing $CP$ asymmetry, leaving only new tensor interactions as a possible mechanism. We demonstrate that, contrary to previous assumptions in the literature, the crucial interference between vector and tensor phases is suppressed by at least 2 orders of magnitude due to Watson’s final-state-interaction theorem. Furthermore, we find that the strength of the relevant $CP$-violating tensor interaction is strongly constrained by bounds from the neutron electric dipole moment and $D–\overline{D}$ mixing. These observations together imply that it is extremely difficult to explain the current $\tau \to K_S\pi {\nu }_{\tau }$ measurement in terms of physics beyond the standard model originating in the ultraviolet.

Figure 1

$|f_{+}(s)/f_{+}(0)|$ from [31] (black solid line) in comparison to the Omnès factor (24) (red dashed line).

Figure 2

${\delta }_{+}$ from a BW approximation for the $K^{*}(892)$ (red dashed line) in comparison to the phase from the experimental fit [31] (blue dot-dashed line). The band represents our estimate of inelastic effects; see the main text for details.

Figure 3

Diagrammatic representation of the electromagnetic dipole operator contributing to the neutron EDM produced by inserting the $(\overline{\tau }{\sigma }_{\mu \nu }R\tau )(\overline{u}{\sigma }^{\mu \nu }Ru)$ operator (left), and the contribution to $D–\overline{D}$ mixing originating from the double insertion of the operator $(\overline{\tau }{\sigma }_{\mu \nu }R\tau )(\overline{c}{\sigma }^{\mu \nu }Ru)$ (right, the second permutation is omitted).

Figure 4

Allowed regions in the $\mathrm{Im}{c}_T^{21}–\mathrm{Im}{c}_T^{11}$ plane from the neutron EDM and $D–\overline{D}$ mixing (for $\varphi =\pm \pi /4$ and $\mathrm{\Lambda }=1\mathrm{TeV}$), compared to the favored region from the $\tau \to K_S\pi {\nu }_{\tau }$ $CP$ asymmetry. The exclusion regions for $\varphi =\pm \pi /4$ differ due to the asymmetric form of the fit result in [53].