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.

This work deals with form factors of the energy-momentum tensor (EMT) of spin-0 particles and the unknown particle property D-term related to the EMT, and is divided into three parts.The first part explores free, weakly and strongly interacting theories to study EMT form factors with the following findings. (i) The free Klein-Gordon theory predicts for the D-term D = −1.(ii) Even infinitesimally small interactions can drastically impact D. (iii) In strongly interacting theories one can encounter large negative D though notable exceptions exist, which includes Goldstone bosons of chiral symmetry breaking. (iv) Contrary to common belief one cannot arbitrarily add "total derivatives" to the EMT. Rather the EMT must be defined in an unambiguous way.The second part deals with the interpretation of the information content of EMT form factors in terms of 3D-densities with following results. (i) The 3D-density formalism is internally consistent.(ii) The description is subject to relativistic corrections but those are acceptably small in phenomenologically relevant situations including nucleon and nuclei. (iii) The free field result D = −1 persists when a spin-0 boson is not point-like but "heuristically given some internal structure."The third part investigates the question, whether such "giving of an extended structure" can be implemented dynamically, and has the following insights. (i) We construct a consistent microscopic theory which, in a certain parametric limit, interpolates between extended and point-like solutions.(ii) This theory is exactly solvable which is rare in 3 + 1 dimensions, admits non-topological solitons of Q-ball-type, and has a Gaussian field amplitude. (iii) The interaction of this theory belongs to a class of logarithmic potentials which were discussed in literature, albeit in different contexts including beyond standard model phenomenology, cosmology, and Higgs physics.

The D-term is defined through matrix elements of the energy-momentum tensor, similarly to mass and spin, yet this important particle property is experimentally not known any fermion. In this work we show that the D-term of a spin 1 2 fermion is of dynamical origin: it vanishes for a free fermion. This is in pronounced contrast to the bosonic case where already a free spin-0 boson has a non-zero intrinsic D-term. We illustrate in two simple models how interactions generate the D-term of a fermion with an internal structure, the nucleon. All known matter is composed of elementary fermions. This indicates the importance to study this interesting particle property in more detail, which will provide novel insights especially on the structure of the nucleon.

The form factors of the energy-momentum tensor can be accessed via studies of generalized parton distributions in hard exclusive reactions. In this talk we present recent results on the energymomentum tensor form factors and densities in the bag model formulated in the large-N c limit. The simplicity and lucidity of this quark model allow us to investigate many general concepts which have recently attracted interest, including pressure, shear forces and angular momentum density inside the nucleon. The results from the bag model are theoretically consistent, and comply with all general requirements.

The probably most fundamental information about a particle is contained in the matrix elements of its energy momentum tensor (EMT) which are accessible from hard-exclusive reactions via generalized parton distribution functions. The spin decomposition of the nucleon and Ji sum rule are one example. Less prominent but equally important information is encoded in the stress tensor, related to the spatial components of the EMT, which shows in detail how the strong forces inside the nucleon balance to form a bound state. This provides not only unique insights on nucleon structure. It also leads to fascinating new applications to hadron spectroscopy which allow us to formulate new interpretations of the charmonium-nucleon pentaquarks discovered by LHCb. Recent progress is reviewed in this short overview article.