Doubly CKM-suppressed corrections to CP asymmetries in B⁰ to J/psi K⁰

A doubly CKM-suppressed amplitude in $B^0\to J/\psi K_S$ leads to corrections in CP asymmetries $S = \sin 2\beta, C=0$, which may be enhanced by long-distance rescattering. It has been suggested that this enhancement may lead to several percent corrections. We calculate an upper bound of order $10^{-3}$ on rescattering corrections using measured branching ratios for charmless $|\Delta S|=1$ $B^0$ decays.