SU(3) relations and the CP asymmetries in B decays to ηK_S, ΦK_S, and K⁺K^- K_S

We consider CP asymmetries in neutral B meson decays to ηK_S, ΦK_S, and K⁺K^- K_S. We use SU(3) relations to estimate or bound the contributions to these amplitudes proportional to V*_ubV_us. Such contributions induce a deviation of the S_f terms measured in these time dependent CP asymmetries from that measured for ψK_S. For the K ⁺K^-K_S mode, we estimate the deviation to be of order 0.1. For the η′ K_S mode, we obtain an upper bound on this deviation of order 0.3. For the ΦK_S mode, we have to add a mild dynamical assumption to the SU(3) analysis due to insufficient available data, yielding an upper bound of order 0.25. These bounds may improve significantly with future data. While they are large at present compared to the usually assumed standard model contribution, they are obtained with minimal assumptions and hence provide more rigorous tests for new physics. If measurements yield |S_f- S_ΦKK| that are much larger than our bounds, it would make a convincing case for new physics.