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 Poincaré 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.
Highlights
In QCD the phenomenon of confinement prevents quarks and gluons to appear in the physical spectrum
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 Poincaré symmetry
It is essential to consider the renormalization of the lattice operators before providing any physical interpretation. (Note that E2 and B2 in eq (6.12) do not have the same meaning as the corresponding renormalized operators in the continuum.) This is crucial for the components of the energy-momentum tensor (EMT) since the breaking of Poincaré symmetry on the lattice is a source of artifacts, as we will see in the following
Summary
In QCD the phenomenon of confinement prevents quarks and gluons to appear in the physical spectrum. [5], which concluded that the above two decompositions mix information about mass with the constraint of mechanical equilibrium Keeping these two aspects of the hadronic bound state physics separated, one obtains a natural decomposition of the hadron mass into a quark contribution and a gluon contribution. We present further details on the virial theorem and its physical meaning in various contexts in appendix A, and give a brief account of the DR approach in appendix B
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