Testing the superweak theory ofCPviolation in neutralBdecays

In order to rule out the superweak theory for $\mathrm{CP}$ violation, future experiments will try to find a difference between the $\mathrm{CP}$-violating asymmetries in the decays $B^0\to \psi K_S$ and $B^0\to {\pi }^{+}{\pi }^{-}$. However, Winstein recently noted that, for some acceptable values of the Cabibbo-Kobayashi-Maskawa parameters, the standard model would give equal asymmetry parameters for these decays just as the superweak theory does. In this paper we show that, by considering both tree and penguin contributions to the decay amplitudes, the test can still be effective if a third asymmetry is measured with enough precision.