Electromagnetic gauge invariance of chiral hybrid quark models

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Abstract
In this work, we investigate the question whether the conventional analysis of the electromagnetic form factors of the nucleon, evaluated in the framework of the cloudy bag model (CBM) or other chirally invariant hybrid quark models utilizing the same philosophy, is gauge invariant? In order to address that point, we first formulate the CBM in a style that resembles the technique of loop integrals. Evaluating the self-energy and the electromagnetic form factors of the nucleon in that manner, and comparing with the standard analysis where nonrelativistic perturbation theory is used, allows us to show that our approach is appropriate and to point out what approximations are made in the standard derivation of the model. From the form of those loop integrals, we then show that additional diagrams are needed to preserve electromagnetic gauge invariance and we assess the corresponding corrections.
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