Energy-momentum tensor in $\Phi^4$ theory at one loop

The energy-momentum tensor form factors are studied in $\Phi^4$ theory to one-loop order with particular focus on the $D$-term, a particle property which has attracted a lot of attention in the recent literature. It is shown that the free Klein-Gordon theory value of the $D$-term $D_{\text{free}}=-1$ is reduced to $D_{\text{one-loop}} =-\frac13$ even if the $\Phi^4$ interaction is infinitesimally small. A companion work in $\Phi^3$ theory confirms this result which may indicate that it is independent of the type of interaction as long as the scalar theory is renormalizable. Dispersion relations are studied. Various definitions of mean square radii including the mechanical radius are investigated. The findings contribute to a better understanding of the EMT properties of particles and their interpretation.