Abstract
We argue that the standard decompositions of the hadron mass overlook pressure effects, and hence should be interpreted with great care. Based on the semiclassical picture, we propose a new decomposition that properly accounts for these pressure effects. Because of Lorentz covariance, we stress that the hadron mass decomposition automatically comes along with a stability constraint, which we discuss for the first time. We show also that if a hadron is seen as made of quarks and gluons, one cannot decompose its mass into more than two contributions without running into trouble with the consistency of the physical interpretation. In particular, the so-called quark mass and trace anomaly contributions appear to be purely conventional. Based on the current phenomenological values, we find that in average quarks exert a repulsive force inside nucleons, balanced exactly by the gluon attractive force.
Highlights
According to the standard model of particle physics, the masses of almost all known elementary particles are generated through the Brout–Englert–Higgs (BEH) mechanism
In order to address the question of the origin of the hadron mass, one should rather start from the energy-momentum tensor (EMT) of Quantum Chromodynamics (QCD)
We used forward matrix elements of the energy-momentum tensor to characterize static mechanical properties of hadrons. The components of such an energy-momentum tensor can be interpreted semi-classically in terms of parton energy density and pressure averaged over time and the hadron proper volume
Summary
According to the standard model of particle physics, the masses of almost all known elementary particles are generated through the Brout–Englert–Higgs (BEH) mechanism. Lattice QCD calculation of hadron masses obtained from the analysis of correlations functions in Euclidean time is in remarkable agreement with the experimental spectrum [5,6]. This method gives little insight on how these masses arise from quark and gluon contributions. Physics to require the EMT to be symmetric in its Lorentz indices. This aspect will not affect the purpose of the present paper and will not be discussed further. Mass decompositions can be obtained from the expectation value of the EMT. It is more natural to define mass via the normalized expectation value of some spatially extended operator
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