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

Employing the QCD factorization formalism we compute B-u(-) -> gamma* l (nu) over bar (l) form factors with an off-shell photon state possessing the virtuality of order m(b) Lambda(QCD) and m(b)(2), respectively, at next-to-leading order in QCD. Perturbative resummation for the enhanced logarithms of m(b)/Lambda(QCD) 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(-) -> gamma*W* form factors with a hard-collinear photon at O(alpha(0)(s)). We further construct a complete set of the angular observables governing the full differential distribution of the four-body leptonic decays B-u(-) -> l'(l) over bar 'l (nu) over bar (l) with l, l' is an element of {e, mu} 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.