Soft FSI Systematics for charmless strange $B^{\pm }$ Decays

Abstract

New results going beyond those obtained from isospin and flavor symmetry and subject to clear experimental tests are obtained for effects of FSI in $B^{\pm }$ decays to final states containing neutral flavor-mixed mesons like $\omega$, $\varphi$, $\eta$ and ${\eta }^{\prime }$. The most general strong-interaction diagrams containing arbitrary numbers of quarks and gluons are included with the assumptions that any $q\bar{q}$ pair created by gluons must be a flavor singlet, and that there are no hairpin diagrams in which a final meson contains a $q\bar{q}$ pair from the same gluon vertex. The smallness of $K^{-}\eta$ suggests that it might have a large CP violation. A sum rule is derived to test whether the large $K^{-}{\eta }^{\prime }$ requires the addition of an additional glueball or charm admixture. Further analysis from $D_s$ decay systematics supports this picture of FSI and raises questions about charm admixture in the ${\eta }^{\prime }$.