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

Abstract

Employing the QCD factorization formalism we compute $B_u^{-}\to {\gamma }^{\ast }\mathrm{\ell }{\overline{v}}_{\mathrm{\ell }}$ form factors with an off-shell photon state possessing the virtuality of order m_b Λ_QCD and $m_b^2$, respectively, at next-to-leading order in QCD. Perturbative resummation for the enhanced logarithms of m_b/Λ_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 $B_u^{-}\to {\gamma }^{\ast }{W}^{\ast }$ form factors with a hard-collinear photon at $\mathcal{O}\left({\alpha }_s^0\right)$. We further construct a complete set of the angular observables governing the full differential distribution of the four-body leptonic decays $B_u^{-}\to {\mathrm{\ell }}^{\prime }{\overline{\mathrm{\ell }}}^{\prime }\mathrm{\ell }{\overline{v}}_{\mathrm{\ell }}$ 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.