The gauge-invariant canonical energy-momentum tensor

TL;DR

This paper develops a gauge-invariant formulation of the canonical energy-momentum tensor by employing non-local definitions and parametrizations, linking it to measurable parton distributions and deriving new sum rules.

Contribution

It provides the first complete parametrization of the gauge-invariant non-local energy-momentum tensor and connects it to measurable two-parton distribution functions.

Findings

Confirmed the absence of model-independent relations between TMDs and orbital angular momentum.

Recovered the Burkardt sum rule more simply.

Derived three new sum rules for transverse momentum conservation.

Abstract

The canonical energy-momentum tensor is often considered as a purely academic object because of its gauge dependence. However, it has recently been realized that canonical quantities can in fact be defined in a gauge-invariant way provided that strict locality is abandoned, the non-local aspect being dictacted in high-energy physics by the factorization theorems. Using the general techniques for the parametrization of non-local parton correlators, we provide for the first time a complete parametrization of the energy-momentum tensor (generalizing the purely local parametrizations of Ji and Bakker-Leader-Trueman used for the kinetic energy-momentum tensor) and identify explicitly the parts accessible from measurable two-parton distribution functions (TMDs and GPDs). As by-products, we confirm the absence of model-independent relations between TMDs and parton orbital angular momentum, recover in a much simpler way the Burkardt sum rule and derive three similar new sum rules expressing the conservation of transverse momentum.