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

Abstract

Employing the QCD factorization formalism we compute B − u → γ * ν form factors with an off-shell photon state possessing the virtuality of order m b Λ QCD and m 2 b , 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 → γ * W * form factors with a hard-collinear photon at O(α 0 s ). We further construct the complete set of the angular observables governing the full differential distribution of the four-body leptonic decays B − u → ¯ ν with , ∈ {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.

Enhanced Next-to-Leading-Order Corrections to Weak Annihilation $B$-Meson Decays

“…which can be reduced to a rather compact form G B1 ≈ 18 ln m B λ B + γ E − 2 − i π in the leading-power approximation by employing the Grozin-Neubert model [42] for φ + B (ω) and the asymptotic twist-two distribution amplitudes φ M2 (x) and φ M1 (y). The dimensionful quantity λ −1 B represents the inverse moment of the above HQET distribution amplitude [40,42,49] and serves as an indispensable ingredient for the theory description of a wide variety of exclusive bottom-meson decays [48][49][50][51][52][53][54][55][56][57][58]. It is worthwhile to stress that we do not aim at implementing QCD resummation of the perturbatively generated logarithms of m B /λ B , which are nevertheless not numerically significant for the realistic Bq -meson mass.…”

Study of the four-body decays $B^{0}_{S} \rightarrow ππππ$ in the perturbative QCD approach

“…Generally, it is not easy to calculate dynamics of these decays, however, it can be simplified by employing the factorization theorems. Several factorization approaches, such as QCD factorizations (QCDF) [19][20][21][22][23][24][25][26][27], the soft collinear effective theory (SECT) [28][29][30], factorizationassisted topological amplitude approach (FAT) [31] and the perturbative QCD (PQCD) factorization approachs [32][33][34][35][36][37][38][39][40][41][42][43] are used to investigate these decays. Compared with other approaches, the perturbative QCD factorization which based on K T factorization theorem is more appropriate to find out the four-body decays of B meson [44][45][46].…”