Angular distribution and CP asymmetries in the decays $\overline{B}\to K^{-}{\pi }^{+}{e}^{-}{e}^{+}$ and $\overline{B}\to {\pi }^{-}{\pi }^{+}{e}^{-}{e}^{+}$

The short-distance Hamiltonian describing $\overrightarrow{b}{s\left(d\right)e}^{-}{e}^{+}$ in the standard model is used to obtain the decay spectrum of $\overline{B}\to K^{-}{\pi }^{+}{e}^{-}{e}^{+}$ and $\overline{B}\to {\pi }^{-}{\pi }^{+}{e}^{-}{e}^{+},$ assuming the $K\pi$ and $\pi \pi$ systems to be the decay products of $K^{*}$ and $\rho$ respectively. The specific features calculated are (i) the angular distribution of $K^{-}$ (or ${\pi }^{-})$ in the $K^{-}{\pi }^{+}$ (or ${\pi }^{-}{\pi }^{+})$ center-of-mass (c.m.) frame, (ii) the angular distribution of $e^{-}$ in the $e^{-}{e}^{+}$ c.m. frame, and (iii) the correlation between the meson and lepton planes. We also derive $\mathit{CP}$-violating observables obtained by combining the above decays with the conjugate processes $\overrightarrow{B}{K}^{+}{\pi }^{-}{e}^{-}{e}^{+}$ and $\overrightarrow{B}{\pi }^{-}{\pi }^{+}{e}^{-}{e}^{+}.$