The Possibility of Large Direct CP Violation in B to K pi-Like Modes Due to Long Distance Rescattering Effects and Implications for the Angle gamma

We consider the strong rescattering effects that can occur in the decays such as B -> K pi, K* pi, K rho… and their impact on direct CP violation in these modes. First we discuss, in general, how the CPT theorem constrains the resulting pattern of partial rate asymmetries leading to different brands of direct CP. Traditional discussions have centered around the absorptive part of the penguin graph which has Delta I=0 in b -> s transitions and as a result causes simple'' CP violation; long-distance final state rescattering effects, in general, will lead to a different pattern of CP: compound’’ CP violation. Predictions of simple CP are quite distinct from that of compound CP. Final states rescattering phases in B decays are unlikely to be small possibly causing large compound CP violating partial rate asymmetries in these modes. CPT theorem requires a cancellation of PRA due to compound CP amongst the $K\pi$ states themselves; thus there can be no net cancellation with other states such as K*\pi, K\rho etc. Therefore, each class of such modes, namely K pi, K rho, K^*pi, K a_1 etc. can have large direct CP emanating from rescattering effects. Various repercussions for the angle $\gamma$ are also discussed.