Proton Mass Decomposition and Hadron Cosmological Constant

TL;DR

This paper decomposes the proton mass into quark and gluon contributions using lattice QCD, revealing a scheme-invariant structure and linking the glue condensate to a hadron cosmological constant that balances confinement pressure.

Contribution

It provides a scheme- and scale-invariant decomposition of the proton mass and identifies the glue part of the trace anomaly as a vacuum energy contributing to a hadron cosmological constant.

Findings

Proton mass decomposition into quark and gluon fractions using lattice results.

Identification of the glue trace anomaly as vacuum energy from the glue condensate.

The glue condensate's energy acts as a restoring pressure balancing confinement.

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 $\langle H_{\beta}\rangle $ 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 $\langle H_{\beta}\rangle$, gives a {\it constant} restoring pressure which 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 $\langle H_{\beta}\rangle$ 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.