CPviolation in the decayB→Xde+e−

The decay $b\to {\mathrm{de}}^{+}{e}^{-}$ has an amplitude containing comparable contributions proportional to $V_{\mathrm{tb}}{V}_{\mathrm{td}}^{*},$ $V_{\mathrm{cb}}{V}_{\mathrm{cd}}^{*},$ and $V_{\mathrm{ub}}{V}_{\mathrm{ud}}^{*}.$ These pieces involve different unitarity phases produced by c$\overline{c}$ and uū loops. The simultaneous presence of different CKM phases and different dynamical phases leads to a calculable asymmetry in the partial widths of b→${\mathrm{de}}^{+}$ $e^{-}$ and $\overline{b}$→d¯$e^{+}$ $e^{-}$. Using the effective Hamiltonian of the standard model, we calculate this asymmetry as a function of the $e^{+}$ $e^{-}$ invariant mass. The effects of ρ, ω, and J/ψ resonances are taken into account in the vacuum polarization of the uū and c$\overline{c}$ currents. As a typical result, an asymmetry of -5% (-2%) is predicted in the nonresonant domain $1\hspace{0.5em}\mathrm{GeV}<m_{e^{+}{e}^{-}}<m_{J/\psi },$ assuming η=0.34 and ρ=0.3 (-0.3). The branching ratio in this domain is 1.2×${10}^{\mathrm{-}7}$ (3.3×${10}^{\mathrm{-}7}$). Results are also obtained in the region of the J/ψ resonance, where an asymmetry of 3×${10}^{\mathrm{-}3}$ is expected, subject to certain theoretical uncertainties in the b→dJ/ψ amplitude.