The light-front gauge-invariant energy-momentum tensor

TL;DR

This paper introduces a comprehensive parametrization of the gauge-invariant energy-momentum tensor in quantum field theory, clarifying its relation to parton distributions and sum rules, with implications for understanding angular momentum in hadrons.

Contribution

It provides the first complete parametrization of the asymmetric, non-local, gauge-invariant canonical energy-momentum tensor, extending previous work on the symmetric Belinfante-Rosenfeld tensor.

Findings

Explicitly shows two-parton TMDs cannot determine orbital angular momentum independently.

Recovers the Burkardt sum rule.

Derives new sum rules for higher-twist distributions.

Abstract

We provide for the first time a complete parametrization for the matrix elements of the generic asymmetric, non-local and gauge-invariant canonical energy-momentum tensor, generalizing therefore former works on the symmetric, local and gauge-invariant kinetic energy-momentum tensor also known as the Belinfante-Rosenfeld energy-momentum tensor. We discuss in detail the various constraints imposed by non-locality, linear and angular momentum conservation. We also derive the relations with two-parton generalized and transverse-momentum dependent distributions, clarifying what can be learned from the latter. In particular, we show explicitly that two-parton transverse-momentum dependent distributions cannot provide any model-independent information about the parton orbital angular momentum. On the way, we recover the Burkardt sum rule and obtain similar new sum rules for higher-twist distributions.