Energy momentum tensor on and off the light cone: exposition with scalar Yukawa theory

TL;DR

This paper computes gravitational form factors in scalar Yukawa theory using both light-cone and covariant perturbation theory at one-loop, highlighting the advantages and challenges of the light-cone approach.

Contribution

It demonstrates how to extract gravitational form factors from the light-front energy-momentum tensor and identifies the 'good currents' suitable for renormalization and analysis.

Findings

Light-cone formalism offers a potential method beyond perturbation theory.

Certain components of the energy-momentum tensor are suitable for form factor extraction.

Comparison clarifies the role of Poincaré symmetry in different formalisms.

Abstract

We compute the gravitational form factors $A_i$, $D_i$ and $\bar c_i$ of the scalar Yukawa theory using both the light-cone and covariant perturbation theory at the one-loop level. The light-cone formalism provides a potential approach to access these form factors beyond the perturbative regime. However, unlike the covariant formulation, the Poincar\'e symmetry on the light cone is not manifest. In this work, we use perturbation theory as a benchmark to extract the gravitational form factors from the light-front energy-momentum tensor. By comparing results on and off the light cone, we identify $T^{++}, T^{+a}, T^{+-}, T^{12}$ as the "good currents" that are properly renormalized and can be used to extract the gravitational form factors.