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.
Highlights
The matrix elements of the energy-momentum tensor (EMT), Tμν, [1] can be explored through studies of generalized parton distribution functions in hard exclusive reactions [2,3] and contain information on the basic properties of a particle: mass, spin, and the important but far less known D-term [4]
The information content of EMT form factors is visualized in terms of EMT densities [5] which allow us to learn about properties like energy density, angular momentum distribution, or internal forces in hadrons [5,6,7,8,9,10,11]
EMT properties were studied in hadronic models, chiral perturbation theory, lattice QCD and other strongly interacting systems [12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53] which had one common feature: these systems were governed by short-range forces
Summary
The matrix elements of the EMT, Tμν, [1] can be explored through studies of generalized parton distribution functions in hard exclusive reactions [2,3] and contain information on the basic properties of a particle: mass, spin, and the important but far less known D-term [4]. Classical models of an extended electric charge have a long history dating back to the works of Abraham and Lorentz [54,55] It was recognized by Poincarethat in order to compensate the electrostatic repulsion one must introduce cohesive forces, known as Poincarestresses [56], which were introduced in an ad hoc manner [54,55,56,57,58,59,60]. [61] used in this work is to the best of our knowledge the first fully consistent classical model of an extended charged particle where the Poincarestresses are generated dynamically in a local, relativistic, classical field theory.
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