$\mathrm{CP}$ violation in the decays $B^0\to \Psi K_S$ and $B^0\to {\pi }^{+}{\pi }^{-}$: A probe for new physics

We point out the strong correlation between the $\mathrm{CP}$-violating asymmetries in the decays $B^0\to \Psi K_s$ and $B^0\to {\pi }^{+}{\pi }^{-}$ that is predicted by the Kobayashi-Maskawa model. This results in a very restricted allowed region for the asymmetries, and so their measurement will provide a powerful test of the standard model. To show how new physics may give very different results, we look at the predictions of a simple model where both the standard model and superweak contributions to the $K^0$ and $B^0$ mass matrices coexist. We find that, for possible values of the parameters, practically any values are allowed for the asymmetries.