Energy momentum tensor and the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi></mml:math> term in the bag model
M. J. Neubelt, A. Sampino, Jonathan Hudson, Kemal Tezgin, P. Schweitzer
Abstract
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 ${N}_{c}$ and show that the EMT form factors are consistently described in this model in the large-${N}_{c}$ 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 the $\ensuremath{\rho}$-meson, Roper resonance, other ${N}^{*}$ states, and $\mathrm{\ensuremath{\Delta}}$-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.