QCD factorization of the four-lepton decay $$B^-→ \ell \bar{ν }_\ell \ell ^{(′ )} \bar{\ell }^{(′ )}$$ B - → ℓ ν ¯ ℓ ℓ ( ′ ) ℓ ¯ ( ′ ) - Martin Beneke; Philipp Böer; Panagiotis Rigatos; K. Keri Vos (European Physical Journal C: Particles and Fields, 2021)
Abstract Motivated by the first search for the rare charged-current B decay to four leptons, $$\ell \bar{ν }_\ell \ell ^{(′ )} \bar{\ell }^{(′ )}$$ ℓ ν ¯ ℓ ℓ ( ′ ) ℓ ¯ ( ′ ) , we calculate the decay amplitude with factorization methods. We obtain the $$B→ γ ^*$$ B → γ ∗ form factors, which depend on the invariant masses of the two lepton pairs, at leading power in an expansion in $$Λ _QCD/m_b$$ Λ QCD / m b to next-to-leading order in $$α _s$$ α s , and at $$\mathcal {O}(α _s^0)$$ O ( α s 0 ) at next-to-leading power. Our calculations predict branching fractions of a few times $$10^{-8}$$ 10 - 8 in the $$\ell ^{(′ )} \bar{\ell }^{(′ )}$$ 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 $$λ _B$$ 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 $$λ _B$$ λ B is almost comparable to $$B^- → \mathrm {\ell }^- \bar{ν }_{\mathrm {\ell }}γ $$ B - → ℓ - ν ¯ ℓ γ when $$λ _B$$ 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 .