Pseudoscalar and scalar operators of Higgs penguin diagrams in the MSSM and $B\rightarrow\phi K\ast, K \eta(\prime)$ decays
Hisaki Hatanaka and Kwei-Chou Yang

We study the effect of $b\to s\sbar s$ scalar/pseudoscalar operators in $B\to K\eta^{(\prime)},\,\phi K^*$ decays. In the minimal supersymmetric standard model (MSSM), such scalar/pseudoscalar operators can be induced by the penguin diagrams of neutral Higgs bosons. These operators can be Fierz-transformed into tensor operators, and the resultant tensor operators could affect the transverse polarization amplitudes in $B\to \phi K^*$ decays. A combined analysis of the decays $B\to \phi K^*$ and $B \to K\eta^{(\prime)}$, including $b\to s\bar{s}s$ scalar/pseudoscalar operators and their Fierz-transformed tensor operators originated from the MSSM, is performed. Our study is based on the followings: (1) Assuming that weak annihilations in $B\to\phi K^*$ is negligible and the polarization puzzle is resolved by Fierz-transformed tensor operators, it results in too large coefficients of scalar/pseudoscalar operators, such that the resulting $B\to K\eta^{(\prime)}$ branching fractions are much larger than observations. (2) When we take the weak annihilations in $B \to \phi K^*$ into account, the polarization puzzle can be resolved. In this case, new physics effects are strongly suppressed and no more relevant to the enhancement of the transverse modes in $B\to \phi K^*$ decays.

© 2008 The American Physical Society.