CP-violating effects in heavy-meson systems

We calculate the dilepton charge asymmetry in the neutral-conjugate-heavy-meson systems produced in $e^{+}{e}^{-}$ annihilation. This asymmetry, which is a measure of the intrinsic $\mathrm{CP}$ violation in the mass matrix, is calculated in the Kobayashi-Maskawa (KM) model as well as the Higgs-boson model of $\mathrm{CP}$ nonconservation. While the charge asymmetry is small for the $D^0-{\overline{D}}^0$ and $B^0-{\overline{B}}^0$ systems in both models, it is predicted to be quite large (${10}^{-1\mathrm{}}$-${10}^{-2\mathrm{}}$) in the $T^0-{\overline{T}}^0$ system in the Higgs-boson scheme. Thus if experiments to measure the dilepton asymmetry are feasible (but could be considerably difficult in practice), only the $T^0-{\overline{T}}^0$ system can distinguish between the Higgs-boson-exchange model and the KM model. A $T$-violating polarization of the lepton in the semileptonic decay of a meson cannot arise in the KM model. However, even in the Higgs-boson model the transverse polarization of the muon normal to the decay plane in the semileptonic kaon decay although nonzero is still quite small (at the level ∼ ${10}^{-4\mathrm{}}$) unless the ratio of the two vacuum expectation values $\frac{{v_2}^2}{{v_3}^2}$ is unexpectedly large. The $T$-odd $\tau$-lepton polarization in $B$-meson decay is expected to be ∼ ${10}^{-2\mathrm{}}$, thus conceivably measurable.