6533b7dbfe1ef96bd1270cb0

RESEARCH PRODUCT

Hadron structure in the description of electromagnetic reactions

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The description of electromagnetic reactions at intermediate energies, such as pion electroproduction or (virtual) Compton scattering, traditionally starts from covariant tree-level Feynman diagrams (Born or pole terms). Internal hadron structure is included by means of (on-shell) form factors in the vertices while free propagators are used. To overcome problems with gauge invariance, simple prescriptions, such as, choosing ${F}_{1}^{V}{(q}^{2}{)=F}_{\ensuremath{\pi}}{(q}^{2})$ in pion electroproduction or the ``minimal substitution,'' are used. We discuss the inherent assumptions of such approaches and study the general structure of electromagnetic vertices and propagators for pions and nucleons. We show which part of the vertex is entirely determined through the Ward-Takahashi identity and point out that detailed features of the ${q}^{2}$ dependence of the form factors cannot be derived from this condition. Recipes to enforce gauge invariance, including the minimal substitution, are critically examined in the light of the exact treatment. The interplay between irreducible contact terms and ``off-shell effects'' in vertices and propagators is demonstrated for real Compton scattering on a pion. The need for a consistent microscopic treatment of reaction amplitudes is stressed and illustrated by an example in the framework of chiral perturbation theory. Shortcomings of the minimal substitution method when applied to effective Lagrangians are pointed out.