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

TL;DR

This paper investigates the one-loop corrections to the energy-momentum tensor form factors in  theory, revealing a significant reduction in the D-term from the free theory value, with implications for understanding particle properties.

Contribution

It demonstrates that the D-term in  theory decreases from -1 to -1/3 at one-loop order, suggesting this may be a universal feature of scalar renormalizable theories.

Findings

The D-term reduces from -1 to -1/3 at one-loop order.

The result is consistent across  and  theories, indicating universality.

Various definitions of mean square radii are analyzed.

Abstract

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.