Proton mass decomposition and hadron cosmological constant

Abstract

Lattice results on sigma terms and global analysis of parton momentum fractions are used to give the quark and glue fractions of the proton mass and rest energy. The mass decomposition in terms of the trace of the energy-momentum tensor is renormalization group invariant. The decomposition of the rest energy from the Hamiltonian and the gravitational form factors are scheme and scale dependent. The separation of the energy-momentum tensor into the traceless part, which is composed of the quark and glue parton momentum fractions, and the trace part has the minimum scheme dependence. We identify the glue part of the trace anomaly $⟨{H}_{\ensuremath{\beta}}⟩$ as the vacuum energy from the glue condensate in the vacuum. From the metric term of the gravitational form factors, which is the stress part of the stress-energy-momentum tensor, we find that the trace part of the rest energy, dominated by $⟨{H}_{\ensuremath{\beta}}⟩$, gives a constant restoring pressure that balances that from the traceless part of the Hamiltonian to confine the hadron, much like the cosmological constant Einstein introduced for a static universe. From a lattice calculation of $⟨{H}_{\ensuremath{\beta}}⟩$ in the charmonium, we deduce the associated string tension, which turns out to be in good agreement with that from a Cornell potential, which fits the charmonium spectrum.