Generalized parton distributions

Unraveling hadron structure with generalized parton distributions

Generalized parton distributions have been introduced in recent years as a suitable theoretical tool to study the structure of the nucleon. Unifying the concepts of parton distributions and hadronic form factors, they provide a comprehensive framework for describing the quark and gluon structure of the nucleon. In this review their formal properties and modeling are discussed, summarizing the most recent developments in the phenomenological description of these functions. The status of available data is also presented.

Generalized parton distributions and the structure of the nucleon

Building upon our recent study [G. S. Bali et al., Eur. Phys. J. C 78, 217 (2018)], we investigate the feasibility of calculating the pion distribution amplitude from suitably chosen Euclidean correlation functions at large momentum. We demonstrate in this work the advantage of analyzing several correlation functions simultaneously and extracting the pion distribution amplitude from a global fit. This approach also allows us to study higher-twist corrections, which are a major source of systematic error. Our result for the higher-twist parameter ${\ensuremath{\delta}}_{2}^{\ensuremath{\pi}}$ is in good agreement with estimates from QCD sum rules. Another novel element is the use of all-to-all propagators, calculated using stochastic estimators, which enables an additional volume average of the correlation functions, thereby reducing statistical errors.

Pion distribution amplitude from Euclidean correlation functions: Exploring universality and higher-twist effects

Bilocal light-ray operators which are Lorentz scalars, vectors or antisymmetric tensors, and which appear in various hard scattering QCD processes, are decomposed into operators of definite twist. These operators are harmonic tensor functions and their Taylor expansion consists of (traceless) local light-cone operators with span irreducible representations of the Lorentz group with definite spin j and common geometric twist (= dimension - spin). Some applications concerning the nonforward matrix elements of these operators and the generalization fo conformal light-cone operators of definite twist is considered. The group theoretical background of the method has been made clear.

Decomposition of nonlocal light-cone operators into harmonic operators of definite twist

Decomposition of non-local light-cone operators into harmonic operators of definite twist

Target mass and finite momentum transfer corrections to unpolarized and polarized diffractive scattering

Power corrections of off-forward quark distributions and harmonic operators with definite geometric twist

Using the framework of the nonlocal light-cone expansion a systematic study is performed for the structure of the twist-2 contributions to the virtual Compton amplitude in polarized deep-inelastic nonforward scattering for general nucleon spin with an additional scalar meson in the final state. A useful kinematic parametrization allowing for appropriate triple-valued off-forward parton distribution amplitudes is given. One-variable amplitudes being adapted to the fixed parameters of the extended Bjorken region are introduced by decomposing the Compton amplitude into collinear and noncollinear components. These amplitudes obey Wandzura-Wilczek- and Callan-Gross-like relations. The evolution equations for all the distribution amplitudes are determined showing that the additional meson momentum does not appear in the evolution kernels. The generalization to n outgoing mesons is given.

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Bodo Geyer

Papers

Decomposition of nonlocal light-cone operators into harmonic operators of definite twist

Decomposition of non-local light-cone operators into harmonic operators of definite twist

Target mass and finite momentum transfer corrections to unpolarized and polarized diffractive scattering

Power corrections of off-forward quark distributions and harmonic operators with definite geometric twist

Structure of the virtual Compton amplitude with an additional final-state meson in the extended Bjorken region