Effects of long-range forces on the D-term and the energy-momentum structure

TL;DR

This paper investigates how long-range electromagnetic forces influence the energy-momentum tensor's D-term and internal force structure in hadrons, revealing the need for revised definitions in such contexts.

Contribution

It introduces a classical field model to analyze the impact of long-range forces on the D-term, highlighting differences from short-range force systems.

Findings

Long-range forces alter the traditional interpretation of the D-term.

A more careful definition of the D-term is necessary when long-range interactions are present.

Long-range electromagnetic effects introduce new features in hadron internal force analysis.

Abstract

The hadronic form factors of the energy-momentum tensor (EMT) have attracted considerable interest in recent literature. This concerns especially the D-term form factor D(t) with its appealing interpretation in terms of internal forces. With their focus on hadron structure, theoretical studies so far have concentrated on strongly interacting systems with short-range forces. Effects on the EMT due to long-range forces like the electromagnetic interaction have not yet been studied. Electromagnetic forces play a small role in the balance of forces inside the proton, but their long-range nature introduces new features which are not present in systems with short-range forces. We use a simple but consistent classical field theoretical model of the proton to show how the presence of long-range forces alters some notions taken for granted in short-range systems. Our results imply that a more careful definition of the D-term is required when long-range forces are present.