Heavy-to-light transition form factors at large recoil energy of the light meson have been conjectured to obey a factorization formula, where the set of form factors is reduced to a smaller number of ...universal form factors up to hard-scattering corrections. In this paper we extend our previous investigation of heavy-to-light currents in soft-collinear effective theory to final states with invariant mass
Λ
2 as is appropriate to exclusive
B meson decays. The effective theory contains soft modes and two collinear modes with virtualities of order
m
b
Λ (“hard-collinear”) and
Λ
2. Integrating out the hard-collinear modes results in the hard spectator-scattering contributions to exclusive
B decays. We discuss the representation of heavy-to-light currents in the effective theory after integrating out the hard-collinear scale, and show that the previously conjectured factorization formula is valid to all orders in perturbation theory. The naive factorization of matrix elements in the effective theory into collinear and soft matrix elements may be invalidated by divergences in convolution integrals. In the factorization proof we circumvent the explicit regularization of endpoint divergences by a definition of the universal form factors that includes hard-collinear, collinear and soft effects.
We present a simple empirical parameterization of the x- and t-dependence of generalized parton distributions at zero skewness, using forward parton distributions as input. A fit to experimental data ...for the Dirac, Pauli and axial form factors of the nucleon allows us to discuss quantitatively the interplay between longitudinal and transverse partonic degrees of freedom in the nucleon (“nucleon tomography”). In particular we obtain the transverse distribution of valence quarks at given momentum fraction x. We calculate various moments of the distributions, including the form factors that appear in the handbag approximation to wide-angle Compton scattering. This allows us to estimate the minimal momentum transfer required for reliable predictions in that approach to be around \(\vert t\vert \simeq 3 {\rm GeV}^2\). We also evaluate the valence contributions to the energy-momentum form factors entering Ji’s sum rule.
We present further tests and applications of the new
η–
η′ mixing scheme recently proposed by us. The particle states are decomposed into orthonormal basis vectors in a light-cone Fock ...representation. Because of flavor symmetry breaking the mixing of the decay constants can be identical to the mixing of particle states at most for a specific choice of this basis. Theoretical and phenomenological considerations show that the quark flavor basis has this property and allows, therefore, for a reduction of the number of mixing parameters. A detailed comparison with other mixing schemes is also presented.
In position space the interaction terms of soft-collinear effective theory must be multipole-expanded to obtain interaction terms with homogeneous scaling behaviour. In this Letter we provide a ...manifestly gauge-invariant formulation of the theory after this expansion in the presence of non-Abelian gauge fields, extending our previous result. We give the effective Lagrangian (including the Yang–Mills Lagrangian for collinear and ultrasoft gluons) and heavy-to-light transition currents to second order in the power expansion, paying particular attention to the field redefinitions that lead to the gauge symmetries of the effective Lagrangian.
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.
Within the framework of light-cone quantisation we derive the complete and exact overlap representation of skewed parton distributions for unpolarised and polarised quarks and gluons. Symmetry ...properties and phenomenological applications are discussed.
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