CP violation in the decay B→Xde+e-

The decay b→de+e- has an amplitude containing comparable contributions proportional to VtbVtd*, VcbVcd*, and VubVud*. These pieces involve different unitarity phases produced by c bar c and u bar u loops. The simultaneous presence of different CKM phases and different dynamical phases leads to a calculable asymmetry in the partial widths of b→de+e- and bar b→ bar de+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 u bar u and c bar c currents. As a typical result, an asymmetry of -5% (-2%) is predicted in the nonresonant domain 1 GeV <me+e-<mJ/ψ, assuming η=0.34 and ρ=0.3 (-0.3). The branching ratio in this domain is 1.2x10-7 (3.3x10-7). Results are also obtained in the region of the J/ψ resonance, where an asymmetry of 3x10-3 is expected, subject to certain theoretical uncertainties in the b→dJ/ψ amplitude. copyright 1997 The American Physical Society