Theoretical analysis of the leptonic decays B→ℓℓℓ′̅νℓ′.

We discuss the amplitude of the B→l+l-l′ν′ decays and the differential decay rate d²Γ/dq²dq'2, q the momentum of the l+l- pair emitted from the electromagnetic vertex and q′ the momentum of the l′ν′ pair emitted from the weak vertex. For the relevant form factors, we construct dispersion representations in q², which consistently take into account the Ward identity constraints at q²=0 and the contributions of light vector resonances. This allows a consistent description of the form factors in the range 0<q²≤1 GeV² that saturates around 99% of the decay rate. The differential decay rate behaves at small q² as dΓ(B→l+l-l′ν′)/dq²∝1/q² in the limit m′l=0 but contains also more singular contribution of order m'2l/q4, which we take into account. For the case m′l≤ml, the latter may be neglected, and one obtains a mild logarithmic dependence of Γ(B→l+l-l′ν′) on ml. For the case ml≪m′l, however, the m'2l/q4 terms dominate the decay rate, leading to Γ(B→l+l-l′ν′)∼m'²l/m²l. We find the following features of the four-lepton B decays: i) The decay rates Γ(B→μ+μ-(μνμ,eνe)) are fully dominated by the region of light vector resonances q²≃M²ρ,M²ω. ii) The decay rate Γ(B→e+e-eνe) receives comparable contributions from the region near q²∼4m²e and from the resonance region. iii) One finds a strong enhancement of the decay rate Γ(B→e+e-μνμ)∼m²μ/m²e, which is dominated by the region q²∼4m²e due to the terms O(m²μ/q4) in the differential distribution. [ABSTRACT FROM AUTHOR]