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 ρ-meson, Roper resonance, other N * states and ∆-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.
We present the complete cross-section for the production of unpolarized hadrons in semi-inclusive deep-inelastic scattering up to power-suppressed O(1/Q 2) terms in the Wandzura-Wilczek-type approximation, which consists in systematically assuming thatqgq-terms are much smaller thanqq-correlators. We compute all twist-2 and twist-3 structure functions and the corresponding asymmetries, and discuss the applicability of the Wandzura-Wilczek-type approximations on the basis of available data. We make predictions that can be tested by data from COMPASS, HERMES, Jefferson Lab, and the future Electron-Ion Collider. The results of this paper can be readily used for phenomenology and for event generators, and will help to improve the description of semi-inclusive deep-inelastic processes in terms of transverse momentum dependent parton distribution functions and fragmentation functions beyond the leading twist.
Recently, it is realized that non-perturbative instanton effects can be generated to all orders by perturbation theory around a degenerate minima via Dunne-Ünsal relation in several quantum mechanical systems. In this work we verify the Dunne-Ünsal relation for resonance energy levels of one-dimensional polynomial anharmonic oscillators. We show that the relation is applicable to cubic and quartic anharmonic oscillators which are genus one potentials. However for higher order (higher genus) anharmonic potentials the relation is not satisfied and is subject to a certain extension.
The energy-momentum tensor form factors contain a wealth of information about the nucleon. It is insightful to visualize this information in terms of 3D or 2D densities related by Fourier transformations to the form factors. The densities associated with the angular momentum distribution were recently shown to receive monopole and quadrupole contributions. We show that these two contributions are uniquely related to each other. The quadrupole contribution can be viewed as induced by the monopole contribution, and contains no independent information. Both contributions however play important roles for the visualization of the angular momentum density.
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