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 mb ΛQCD and \( {m}_b^2 \), 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 \( {B}_u^{-}\to {\gamma}^{\ast }{W}^{\ast } \) 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.
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Wang, C., Wang, YM. & Wei, YB. QCD factorization for the four-body leptonic B-meson decays. J. High Energ. Phys. 2022, 141 (2022). https://doi.org/10.1007/JHEP02(2022)141
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DOI: https://doi.org/10.1007/JHEP02(2022)141