Influence of Kaonic Resonances on the CP Violation in $B\to K^*\gamma$Like Processes

Abstract

We consider CP violating effects in decays of the type $B\rightarrow k_i\gamma \rightarrow K\pi\gamma$, $K^*\pi\gamma$ and $K\rho\gamma$, where $k_i$ represents a strange meson resonance. We include in our calculations five of the low-lying resonances with quantum numbers ($J^P$) $1^-$, $1^+$ and $2^+$. At the quark level these decays are driven by the penguin graph as well as tree graphs. CP violation arises due to the difference in the CKM phase between these graphs. We model the final state interaction of the hadronic system using the low lying $k_i$ resonances. We find that radiative decays of B mesons give rise to four of the five kaonic resonances at about $1$ to $7 \%$ of the inclusive $b \rightarrow s \gamma$ rate. We find that the probability of formation of the other three higher resonances is roughly the same as that of $K^*(892)$, which was recently seen at CLEO. In addition to the partial rate asymmetry which arises due to interference between resonances of the same quantum numbers, we show how interference between resonances of the same parity, and also between resonances of the opposite parity, result in two different types of energy asymmetries. CP differential asymmetries at the level of a few percent seem possible. We thus obtain CP violating distributions which may be observed in a sample of about $10^9$\relax $B^\pm$ mesons.