Abstract
Different decompositions (sum rules) for the proton mass have been proposed in the literature. All of them are related to the energy-momentum tensor in quantum chromodynamics. We review and revisit these decompositions by paying special attention to recent developments with regard to the renormalization of the energy-momentum tensor. The connection between the sum rules is discussed as well. We present numerical results for the various terms of the mass decompositions up to 3 loops in the strong coupling, and consider their scheme dependence. We also elaborate on the role played by the trace anomaly and the sigma terms.
Highlights
The most important properties of hadrons are global quantities such as their mass and spin
The mentioned scheme dependence influences the numerics of all the mass decompositions
We focus on the symmetric energy-momentum tensor (EMT) in quantum chromodynamics (QCD) since the antisymmetric part of the EMT does not contribute to forward matrix elements which matter for the mass sum rules
Summary
The most important properties of hadrons are global quantities such as their mass and spin. We emphasize that different (partial) operators showing up in the EMT provide the same forward matrix elements, which makes it difficult to quantify the contribution of a specific operator to the mass decomposition. This feature applies to the operator associated with the EMT trace anomaly. In the Appendix, we give a brief account of the decomposition of the EMT trace into quark and gluon contributions in the minimal subtraction (MS) and modified minimal subtraction (MS) renormalization schemes
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