Systematic approach to exclusive B→Vℓ+ℓ−, Vγ decays

Abstract

We show -by explicit computation of first-order corrections -that the QCD factorization approach previously applied to hadronic two-body decays and to form factor ratios also allows us to compute non-factorizable corrections to exclusive, radiative B meson decays in the heavy quark mass limit. This removes a major part of the theoretical uncertainty in the region of small invariant mass of the photon. We discuss in particular the decays B → K * γ and B → K * ℓ + ℓ − and complete the calculation of corrections to the forward-backward asymmetry zero. The new correction shifts the asymmetry zero by 30%, but the result confirms our previous conclusion that the asymmetry zero provides a clean phenomenological determination of the Wilson coefficient C 9 .

Heavy-to-light currents at NNLO in SCET and semi-inclusive decay

“…We note that the value of the asymmetry zero in semi-inclusive b → sℓ + ℓ − decay is significantly smaller than for the exclusive case [29], where spectator scattering is responsible for a positive shift as is the fact that in this case p + X = 0 in (73). On the other hand the semi-inclusive zero is in the same region as in the inclusive case [39], where virtual effects together with hard gluon bremsstrahlung encoded in functions ω 710 and ω 910 [40] also induce a negative shift on the zero.…”

“…Since the form factor ratio T 1 /V is important for radiative and electroweak penguin decays (see the discussion in Section 5.2 of [14]), the discrepancy between the SCET and QCD sum rules results for R 2 suggests that a dedicated analysis of symmetry breaking corrections to form factors (rather than the form factors themselves) with the QCD sum rule method should be performed. The exclusive decay process B → K * ℓ + ℓ − has been studied in great detail, both with respect to its QCD dynamics [29] and to the sensitivity of various observables to new physics [30], because it can be measured relatively easily at hadron colliders. Also on the inclusive decay processB → X s ℓ + ℓ − dedicated work exists on higher order radiative corrections (see [31] for recent reviews), power corrections [32,33], and on the identification of additional kinematic observables [34].…”

“…However, the study of power corrections in [37] does not cover all such corrections and applies a rather crude treatment to those arising from soft gluon attachments to the charm-loop diagrams by absorbing the 1/m 2 c non-perturbative power corrections into the C incl i , which is justified only in the absence of invariant mass cuts. In the semi-inclusive region, the matrix element of (29) in [33] cannot, due to the presence of a soft gluon, be expressed in terms of a short-distance coefficient times a local matrix element, since the soft gluon attached to the charm loop affects the invariant mass of an energetic hadronic final state by a relevant amount m b Λ QCD , which must be accounted for by a subleading shape function. By treating this correction as in the inclusive case, the authors of [37] implicitly assumed that this shape function somehow factorizes into the local heavy-quark effective theory matrix element λ 2 and the leading-power shape function.…”

B s → Kℓν ℓ and B (s) → π(K)ℓ + ℓ − decays at large recoil and CKM matrix elements

“…We take into account the nonlocal hadronic effects in B → K + − and B → π + − , employing the methods used in [12,13] and originally suggested in [11]. The nonlocal hadronic matrix elements are calculated at spacelike q 2 , using OPE, QCD factorization [14] and LCSRs, and are then matched to their values at timelike q 2 via hadronic dispersion relations. The results of this calculation are reliable at large hadronic recoil, below the charmonium region, that is, at q 2 < m 2 J/ψ .…”

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 .…”