QCD factorization for exclusive non-leptonic B-meson decays: general arguments and the case of heavy–light final states

Abstract

We provide a rigorous basis for factorization for a large class of non-leptonic twobody B-meson decays in the heavy-quark limit. The resulting factorization formula incorporates elements of the naive factorization approach and the hard-scattering approach, but allows us to compute systematically radiative ("non-factorizable") corrections to naive factorization for decays such as B → Dπ and B → ππ. We first discuss the factorization formula from a general point of view. We then consider factorization for decays into heavy-light final states (such as B → Dπ) in more detail, including a proof of the factorization formula at two-loop order. Explicit results for the leading QCD corrections to factorization are presented and compared to existing measurements of branching fractions and final-state interaction phases.

Perturbative corrections to B → D form factors in QCD

“…14) which are well consistent with the fitted values obtained in [5], albeit with the comparably large theory uncertainties for the slop parameter ρ.…”

“…Based upon the canonical behaviour for the B-meson DA φ − B (ω ), one can readily deduce the power counting of f + BD (q 2 ) at large hadronic recoil as O (Λ/m b ) 3/2 from the treelevel sum rules (2.9), different from the scaling law f + BD (q 2 ) ∼ O(1) [14] obtained with the counting scheme m c ∼ m b . In addition, the two form factors f +,0 BD (q 2 ) obtained in the above respect the large-energy symmetry relation as discussed in [35] and the symmetry breaking effects can arise from both perturbative QCD corrections to the short-distance coefficient functions and the subleading power contributions from the higher-twist DA of the B-meson.…”

“…In contrast to the correlation function for the heavy-to-light form factors, the appearance of an additional energy scale (the charm-quark mass) further complicates perturbative QCD factorization for the vacuum-to-B-meson correlation function with an interpolating current for the D-meson. Motivated by the mass hierarchy between the bottom and charm quarks numerically, we will adopt a novel power counting scheme m c ∼ O √ Λ m b , as implemented in the analysis of the inclusive semileptonic B → X c ν decays [11,12] with shape functions of the B-meson, instead of the popular counting scheme m c ∼ O(m b ) widely used in the heavy-quark physics (see, for instance [13,14]). It is then apparent that the on-shell bottom-quark field, the charm-quark field appeared in the interpolating current for the D-meson and the external light-quark field can be identified as hard, hard-collinear and soft modes in QCD following the convention of [15].…”

Three-particle contributions to the renormalisation ofB-meson light-cone distribution amplitudes

“…The case of heavy-light mesons has been discussed only recently [17,18], mainly due to their importance in relation with B-physics, as shown in the case of non-leptonic decays [1][2][3], semileptonic decays [19,20], radiative decays [21][22][23][24][25]. It is possible to define two twoparton distribution amplitudes φ + and φ − from the most simple non-local matrix element: It turns out that only one distribution amplitude, φ + , enters most of the computations considered in the framework of factorisation (non-leptonic decays, B → V γ, B → γℓν) at leading order in 1/m B .…”

“…(2.16)-(2.17), add up as indicated above to B ⊗ z (1) ± and C ⊗ z (1) ± respectively. The combination of the renormalisation constant for the coupling constant and the gluon field tensor is:…”