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^0right) . 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.
Highlights
The QCD perspective, the rare leptonic decays Bu− → ̄ νwith the invariant mass of the lepton pair ( ̄ ) of order mb ΛQCD will further provide us with the valuable information on the inverse moment of the twist-two B-meson distribution amplitude in heavy quark effective theory (HQET), which serves as an indispensable ingredient for the theory description of a variety of the exclusive B-meson decay observables [11–19] based upon the heavy quark expansion as well as the dispersion technique
As the power counting scheme for the virtuality of the photon state dictates factorization properties of the non-hadronic radiative Bu− → γ∗ νdecay form factors, the non-local hadronic matrix element defined by the time-ordered product of the weak transition current uγμ (1 − γ5) b and the bottom-quark electromagnetic current will result in an unsuppressed contribution at p2 ∼ O(m2b ) in the heavy quark expansion
Paper consists in computing the leading-power contributions to the generalized form factors of Bu−(pB) → γ∗(p) (q1) ν (q2) in the heavy quark expansion based upon the soft-collinear effective theory (SCET) approach and the local operator product expansion (OPE) technique at p2 ∼ O(mb ΛQCD) and p2 ∼ O(m2b ) respectively, including the next-to-leading logarithmic (NLL) resummation for the parametrically large logarithms of mb/ΛQCD in the obtained factorization expression with the renormalization-group (RG) formalism
Summary
By analogy with the detailed discussions on the B-meson radiative leptonic decays [5–10], the four-body leptonic Bu− → ̄ νdecay amplitude can be expressed as. The B-meson decay constant in QCD is defined by the local axial-vector matrix element. Constructions of the perturbative factorization formulae for the generalized Bu− → γ∗ transition form factors FV , FA, F1 and F3 constitutes the primary task in predicting the full differential distributions of the four-body leptonic bottom-meson decays. To this end, it proves more convenient to introduce an alternative parametrization of the nonlocal matrix element Tνμ(p, q) for facilitating the practical QCD calculations. It is important to stress that these relations hold to all orders in the perturbative expansion and to all orders in the heavy quark expansion, irrespective of the power-counting behaviour of the off-shell photon momentum
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