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

Abstract

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

Comments: 58 pages, 11 figures