Correlated bounds on CP asymmetries in $B^0 \to \eta' K_S$

Abstract

Flavor SU(3) is used to constrain the coefficients of $\sin\Delta mt$ and $\cos\Delta mt$ in the time-dependent CP asymmetry of $B^0 \to \eta' K_S$. Correlated bounds in the $(S_{\eta' K}, C_{\eta' K})$ plane are derived, by using recent rate measurements of $B^0$ decays into $K^+ K^-, \pi^0\pi^0, \pi^0\eta, \pi^0\eta', \eta\eta, \eta\eta', \eta'\eta'$. Stringent bounds are obtained when assuming a single SU(3) singlet amplitude and when neglecting annihilation-type amplitudes.