Gauging the three-nucleon system

Abstract

We show how to attach an external photon to a system of three strongly interacting nucleons described by three-body scattering equations. Our method involves the idea of gauging the scattering equations themselves, and results in electromagnetic amplitudes where the external photon is effectively coupled to every part of every strong interaction diagram in the model. Current conservation is therefore implemented in the theoretically correct fashion. In this way we obtain the expressions needed to calculate all possible electromagnetic processes of the three-nucleon system including the electromagnetic form factors of the three-body bound state, pd -> pd gamma, gamma He3 -> pd, gamma He3 -> ppn, etc. As the photon is coupled everywhere in the strong interaction model, a unified description of the NNN-gamma NNN system is obtained. An interesting aspect of our results is the natural appearance of subtraction terms needed to avoid the overcounting of diagrams. We have also applied the gauging of equations method to the four-dimensional description of the piNN system which, because of the possibility of pion absorption, has overcounting problems all of its own, and is therefore much more complicated than the NNN case discussed here. Despite these complications, the gauging procedure itself is very simple and leads easily to a unified description of the piNN-gamma piNN system.