QCD factorization of the four-lepton decay B^-→ ℓν¯ _ℓℓ^(′)ℓ¯ ^(′)

Motivated by the first search for the rare charged-current B decay to four leptons, ℓν¯ _ℓℓ^(′)ℓ¯ ^(′), we calculate the decay amplitude with factorization methods. We obtain the B→ γ^∗ form factors, which depend on the invariant masses of the two lepton pairs, at leading power in an expansion in Λ _QCD/ m_b to next-to-leading order in α_s, and at O(αs0) at next-to-leading power. Our calculations predict branching fractions of a few times 10 ^{- 8} in the ℓ^(′)ℓ¯ ^(′) mass-squared bin up to q2=1GeV² with n+q>3GeV. The branching fraction rapidly drops with increasing q². An important further motivation for this investigation has been to explore the sensitivity of the decay rate to the inverse moment λ_B of the leading-twist B meson light-cone distribution amplitude. We find that in the small-q² bin, the sensitivity to λ_B is almost comparable to B^-→ ℓ^-ν¯ _ℓγ when λ_B is small, but with an added uncertainty from the light-meson intermediate resonance contribution. The sensitivity degrades with larger q².