Proton mass decomposition

TL;DR

This paper provides a detailed decomposition of the proton mass into contributions from quark masses, quark energy, glue energy, and trace anomaly using lattice QCD calculations with physical pion mass.

Contribution

It presents the first comprehensive lattice QCD calculation of the proton mass decomposition including quark and glue contributions at physical pion mass.

Findings

Quark masses contribute 9(2)% to the proton mass.

Quark energy contributes 31(5)% and glue energy 37(5)% in the MS scheme.

Quark and glue momentum fractions agree with global analyses.

Abstract

We report the results on the proton mass decomposition and also on the related quark and glue momentum fractions. The results are based on overlap valence fermions on four ensembles of $N_f = 2+1$ DWF configurations with three lattice spacings and volumes, and several pion masses including the physical pion mass. With 1-loop perturbative calculation and proper normalization of the glue operator, we find that the $u, d,$ and $s$ quark masses contribute 9(2)\% to the proton mass. The quark energy and glue field energy contribute 31(5)\% and 37(5)\% respectively in the $\overline{MS}$ scheme at $\mu = 2$ GeV. The trace anomaly gives the remaining 23(1)\% contribution. The $u,d,s$ and glue momentum fractions in the $\overline{MS}$ scheme are consistent with the global analysis at $\mu = 2$ GeV.