The D-term form factor in the presence of electromagnetic long-range forces: a case study in a classical model of the proton*

The prospects of accessing information on the hadronic form factors of the energy-momentum tensor (EMT) have attracted sizable attention in recent literature. This concerns especially the D-term form factor D(t) with its appealing interpretation in terms of internal forces. With the focus on hadron structure, so far theoretical and model studies concentrated on strongly interacting systems with short-range forces and neglected to consider long-range forces like electromagnetic interaction. But the long-range nature of electromagnetic forces introduces features that were not encountered before. We show how the presence of long-range forces alters some notions of the EMT which are taken for granted in short-range systems. We focus our attention on the D-term form factor. The important conclusion is that a more careful definition of the D-term may be required when long-range forces are present.