QCD factorization of the four-lepton decay $$B^-\rightarrow \ell \bar{\nu }_\ell \ell ^{(\prime )} \bar{\ell }^{(\prime )}$$ B - → ℓ ν ¯ ℓ ℓ ( ′ ) ℓ ¯ ( ′ )

Abstract

Abstract Motivated by the first search for the rare charged-current B decay to four leptons, $$\ell \bar{\nu }_\ell \ell ^{(\prime )} \bar{\ell }^{(\prime )}$$ ℓ ν ¯ ℓ ℓ ( ′ ) ℓ ¯ ( ′ ) , we calculate the decay amplitude with factorization methods. We obtain the $$B\rightarrow \gamma ^*$$ B → γ ∗ form factors, which depend on the invariant masses of the two lepton pairs, at leading power in an expansion in $$\Lambda _\mathrm{QCD}/m_b$$ Λ QCD / m b to next-to-leading order in $$\alpha _s$$ α s , and at $$\mathcal {O}(\alpha _s^0)$$ O ( α s 0 ) at next-to-leading power. Our calculations predict branching fractions of a few times $$10^{-8}$$ 10 - 8 in the $$\ell ^{(\prime )} \bar{\ell }^{(\prime )}$$ ℓ ( ′ ) ℓ ¯ ( ′ ) mass-squared bin up to $$q^2=1~$$ q 2 = 1 GeV $$^2$$ 2 with $$n_+q>3~$$ n + q > 3 GeV. The branching fraction rapidly drops with increasing $$q^2$$ q 2 . An important further motivation for this investigation has been to explore the sensitivity of the decay rate to the inverse moment $$\lambda _B$$ λ B of the leading-twist B meson light-cone distribution amplitude. We find that in the small- $$q^2$$ q 2 bin, the sensitivity to $$\lambda _B$$ λ B is almost comparable to $$B^- \rightarrow \mathrm {\ell }^- \bar{\nu }_{\mathrm {\ell }}\gamma $$ B - → ℓ - ν ¯ ℓ γ when $$\lambda _B$$ λ B is small, but with an added uncertainty from the light-meson intermediate resonance contribution. The sensitivity degrades with larger $$q^2$$ q 2 .