[formula presented] violation in the semileptonic [formula presented] decays [formula presented]

Direct (Formula presented) violations in (Formula presented) decays (Formula presented) are investigated within the standard model (SM) and also in its extensions. In the decay processes, we include various excited states as intermediate states decaying to the final hadrons (Formula presented) The (Formula presented) violation within the SM is induced by the interferences between intermediate resonances with different quark flavors. As extensions of the SM, we consider (Formula presented) violations implemented through complex scalar-fermion couplings in the multi-Higgs doublet model and the scalar-leptoquark models. We calculate the (Formula presented)-odd rate asymmetry and the optimal asymmetry. We find that the optimal asymmetry can be measured at the (Formula presented) level with about (Formula presented)-meson pairs in the SM case and (Formula presented)–(Formula presented) pairs in the extended model case, for maximally allowed values of (Formula presented)-odd parameters in each case.