Updated bounds on CP asymmetries in $B^0 \to η' K_S$ and $B^0 \to π^0 K_S$

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New rate measurements of $B^0$ decays into $π^0π^0, π^0η, π^0η', ηη, ηη', η'η'$ and $K^+ K^-$ are used in conjunction with flavor SU(3) to constrain the coefficients $S$ and $C$ of $\sinΔmt$ and $\cosΔmt$ in the time-dependent CP asymmetries of $B^0 \to η' K_S$ and $B^0 \to π^0 K_S$. Experimental values of $S_{η' K}$ are now seen to be closer to the Standard Model expectations, fully consistent with the new improved bounds.
10 pages, 3 figures. To be published in Phys. Rev. D. Discussion and references expanded; data updated

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