QCD factorization of the four-lepton decay (B^-ightarrow ell ar{u }_ell ell ^{(prime )} ar{ell }^{(prime )})

摘要

Motivated by the first search for the rare charged-current B decay to four leptons, $$ell ar{u }_ell ell ^{(prime )} ar{ell }^{(prime )}$$ ? ν ˉ ? ? ( ′ ) ? ˉ ( ′ ) , we calculate the decay amplitude with factorization methods. We obtain the $$Bightarrow gamma ^*$$ 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 $$lpha _s$$ α s , and at $$mathcal {O}(lpha _s^0)$$ O ( α s 0 ) at next-to-leading power. Our calculations predict branching fractions of a few times $$10^{-8}$$ 10 - 8 in the $$ell ^{(prime )} ar{ell }^{(prime )}$$ ? ( ′ ) ? ˉ ( ′ ) mass-squared bin up to $$q^2=1~$$ q 2 = 1 GeV $$^2$$ 2 with $$n_+q3~$$ 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 $$B^- ightarrow mathrm {ell }^- ar{u }_{mathrm {ell }}gamma $$ B - → ? - ν ˉ ? 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 .