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

Abstract

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