An important unresolved question in strong interaction physics concerns the parameterization of power-suppressed long-distance effects to hard processes that do not admit an operator product expansion (OPE). Recently Bauer et al. have developed an effective field theory framework that allows one to formulate the problem of soft-collinear factorization in terms of fields and operators. We extend the formulation of soft-collinear effective theory, previously worked out to leading order, to second order in a power series in the inverse of the hard scale. We give the effective Lagrangian and the expansion of "currents" that produce collinear particles in heavy quark decay. This is the first step towards a theory of power corrections to hard processes where the OPE cannot be used. We apply this framework to heavy-to-light meson transition form factors at large recoil energy.

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 .

We propose a new η-η ′ mixing scheme where we start from the quark flavor basis and assume that the decay constants in that basis follow the pattern of particle state mixing. On exploiting the divergences of the axial vector currents -which embody the axial vector anomaly -all basic parameters are fixed to first order of flavor symmetry breaking. That approach naturally leads to a mass matrix, quadratic in the masses, with specified elements. We also test our mixing scheme against experiment and determine corrections to the first order values of the basic parameters from phenomenology. Finally, we generalize the mixing scheme to include the ηc. Again the divergences of the axial vector currents fix the mass matrix and, hence, mixing angles and the charm content of the η and η ′ . PACS: 14.40.Aq, 11.40.Ha, 11.30.Hv * hep-ph/9802409, Wuppertal WU B 98-2, Heidelberg HD-THEP-98-5 (to be published in Physical Review D) † Supported by Deutsche Forschungsgemeinschaft

Recently it has been shown that symmetries emerging in the heavy quark and large recoil energy limit impose various relations on form factors that parametrise the decay of B mesons into light mesons. These symmetries are broken by perturbative effects. In this paper we discuss the structure of heavy-to-light form factors including such effects and compute symmetry-breaking corrections to first order in the strong coupling. As an application of our results we consider the forwardbackward asymmetry zero in the rare decay B → V ℓ + ℓ − and the possibility to constrain potential new physics contributions to the Wilson coefficient C 9 .

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 |t| ≃ 3 GeV 2 . We also evaluate the valence contributions to the energy-momentum form factors entering Ji's sum rule.