QCD factorization for the four-body leptonic B-meson decays

Abstract

Abstract Employing the QCD factorization formalism we compute $$ {B}_u^{-}\to {\gamma}^{\ast}\mathrm{\ell}{\overline{v}}_{\mathrm{\ell}} $$ B u − → γ ∗ ℓ v ¯ ℓ form factors with an off-shell photon state possessing the virtuality of order mb ΛQCD and $$ {m}_b^2 $$ m b 2 , respectively, at next-to-leading order in QCD. Perturbative resummation for the enhanced logarithms of mb/ΛQCD in the resulting factorization formulae is subsequently accomplished at next-to-leading logarithmic accuracy with the renormalization-group technique in momentum space. In particular, we derive the soft-collinear factorization formulae for a variety of the subleading power corrections to the exclusive radiative $$ {B}_u^{-}\to {\gamma}^{\ast }{W}^{\ast } $$ B u − → γ ∗ W ∗ form factors with a hard-collinear photon at $$ \mathcal{O}\left({\alpha}_s^0\right) $$ O α s 0 . We further construct a complete set of the angular observables governing the full differential distribution of the four-body leptonic decays $$ {B}_u^{-}\to {\mathrm{\ell}}^{\prime }{\overline{\mathrm{\ell}}}^{\prime}\mathrm{\ell}{\overline{v}}_{\mathrm{\ell}} $$ B u − → ℓ ′ ℓ ¯ ′ ℓ v ¯ ℓ with ℓ, ℓ′ ∈ {e, μ} and then perform an exploratory phenomenological analysis for a number of decay observables accessible at the LHCb and Belle II experiments, with an emphasis on the systematic uncertainties arising from the shape parameters of the leading-twist B-meson light-cone distribution amplitude in heavy quark effective theory.