Energy-momentum tensor in QCD: nucleon mass decomposition and mechanical equilibrium

TL;DR

This paper reviews recent advances in understanding the nucleon mass decomposition in QCD, focusing on the energy-momentum tensor, the virial theorem, and the role of anomalies and symmetries in mechanical equilibrium.

Contribution

It provides a detailed analysis of the QCD energy-momentum tensor renormalization, clarifies the interpretation of its components, and refutes the concept of quantum anomalous energy as a mass contribution.

Findings

Quantum anomalous energy is not a genuine mass contribution.

The virial theorem in quantum field theory informs nucleon mass decomposition.

Poincaré symmetry constrains the interpretation of energy components.

Abstract

We review and examine in detail recent developments regarding the question of the nucleon mass decomposition. We discuss in particular the virial theorem in quantum field theory and its implications for the nucleon mass decomposition and mechanical equilibrium. We reconsider the renormalization of the QCD energy-momentum tensor in minimal-subtraction-type schemes and the physical interpretation of its components, as well as the role played by the trace anomaly and Poincar\'e symmetry. We also study the concept of "quantum anomalous energy" proposed in some works as a new contribution to the nucleon mass. Examining the various arguments, we conclude that the quantum anomalous energy is not a genuine contribution to the mass sum rule, as a consequence of translation symmetry.