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

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 DðtÞ with its appealing interpretation in terms of internal forces. With their focus on hadron structure, theoretical studies so far have concentrated mainly 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 longrange forces are present.

Forces within hadrons on the light front

“…A few pertinent properties of the flow and pure stress tensors allow us to identify terms in Eqs. (26,28) with V µν LF (0) and S µν LF (0). First, since the hadron is in equilibrium, the flow and pure stress tensors are separately conserved, meaning the Lorentz structures associated with each should contract with ∆ µ to zero.…”

“…Several phenomenological parametrizations and model calculations of the gravitational form factors A(t) and D(t) for various mesons and baryons exist in the literature (see Refs. [23][24][25][26]43] for instance). Although it is not universal, it is fairly common to use a multipole parametrization to approximate the results of model calculations.…”

“…Investigations into both the EMT and into deeply virtual Compton scattering have led to the discovery [17] of an additional form factor D(t), called the "D-term" or "Druck-term" [18], which does not encode a conserved current, but instead contains information about the spatial distribution of forces within the hadron [19]. The D-term has attracted a lot of interest lately [19][20][21][22][23][24][25][26], and remains largely experimentally unexplored.…”

The gravitational form factor D(t) of the electron

“…Finally, for λ = 0 the long-distance behaviour of the pressure and shear distributions is known [35] -see also the discussion in Ref. [36]. Specifically, one has and…”

“…The form factor D(t), and its Fourier transform in position space, have also been studied using effective field theory by focusing on the region of small |t| (or large distances) [35]. The potential impact of the QED long-distance contribution on D(t) of the proton has been highlighted recently [36]. Furthermore, the QED GFFs of the electron have attracted new interest in order to explore its angular momentum [37,38] and mass structure [39].…”