Abstract
Direct CP violations in $B_{l4}$ decays ($B^\pm \to \pi^+\pi^- l^\pm {\nu}_l$) 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, $\pi^+ + \pi^-$. The CP violation within the SM is induced by the interferences between intermediate resonances with different quark flavors. As extensions of the SM, we consider CP violations implemented through complex scalar-fermion couplings in the multi-Higgs doublet model and the scalar-leptoquark models. We calculate the CP-odd rate asymmetry and the optimal asymmetry. We find that the optimal asymmetry can be measured at $1\sigma$ level with about $10^9$ $B$-meson pairs in the SM case and $10^3$--$10^7$ pairs in the extended model case, for maximally-allowed values of CP-odd parameters in each case.
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