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Register a new userEffects of long-range forces on the D-term and the energy-momentum structure
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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.
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The energy-momentum tensor (EMT) form factors pave new ways for exploring hadron structure. Especially the D-term related to the EMT form factor D(t) has received a lot of attention due to its attractive physical interpretation in terms of mechanical properties. We study the nucleon EMT form factors and the associated densities in the bag model which we formulate for an arbitrary number of colors Nc and show that the EMT form factors are consistently described in this model in the large-Nc limit. The simplicity of the model allows us to test in a lucid way many theoretical concepts related to EMT form factors and densities including recently introduced concepts like normal and tangential forces, or monopole and quadrupole contributions to the angular momentum distribution. We also study the D-terms of rho-meson, Roper resonance, other N* states and Delta-resonances. Among the most interesting outcomes is the lucid demonstration of the deeper connection of EMT conservation, stability, the virial theorem and the negative sign of the D-term.
Couplings between standard model particles and unparticles from a nontrivial scale invariant sector can lead to long range forces. If the forces couple to quantities such as baryon or lepton (electron) number, stringent limits result from tests of the gravitational inverse square law. These limits are much stronger than from collider phenomenology and astrophysics.
The D-term is a fundamental particle property which is defined through the matrix elements of the energy-momentum tensor and as such in principle on equal footing with mass and spin. Yet the experimental information on the D-term of any hadron is very scarce. The D-term of the nucleon can be inferred from studies of hard-exclusive reactions, and its measurement will give valuable insights on the dynamics, structure, and the internal forces inside the nucleon. We review the latest developments and the fascinating applications of the D-term and other energy-momentum tensor (EMT) form factors. We also suggest a definition of the mechanical mean square radius and make a prediction for its size.
We apply renormalisation-group methods to two-body scattering by a combination of known long-range and unknown short-range potentials. We impose a cut-off in the basis of distorted waves of the long-range potential and identify possible fixed points of the short-range potential as this cut-off is lowered to zero. The expansions around these fixed points define the power countings for the corresponding effective field theories. Expansions around nontrivial fixed points are shown to correspond to distorted-wa
We analyze the electromagnetic scattering of massive particles with and without spin and, using the techniques of effective field theory, we isolate the leading long distance effects beyond one photon exchange, both classical and quantum mechanical. Spin-independent and spin-dependent effects are isolated and shown to have a universal structure.
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