Correlated bounds on CP asymmetries in $B^0\to {\eta }^{\prime }{K}_S$

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 $B^0\to {\eta }^{\prime }{K}_S$. Correlated bounds in the $(S_{{\eta }^{\prime }K},C_{{\eta }^{\prime }K})$ plane are derived, by using recent rate measurements of $B^0$ decays into $K^{+}{K}^{-},{\pi }^0{\pi }^0,{\pi }^0\eta ,{\pi }^0{\eta }^{\prime },\eta \eta ,\eta {\eta }^{\prime },{\eta }^{\prime }{\eta }^{\prime }$. Stringent bounds are obtained when assuming a single SU(3) singlet amplitude and when neglecting annihilation-type amplitudes.

Comments: 11 pages, one figure. Version submitted to Physics Letters B. Typo corrected; some text added toward end of Introduction