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=1GeV ² with n+q>3GeV. The branching fraction rapidly drops with increasing q ². 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-q ² 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 q ².