Proton Mass Decomposition from the QCD Energy Momentum Tensor

TL;DR

This study decomposes the proton mass into quark and gluon contributions using lattice QCD, revealing the significant roles of energy components and trace anomaly, with results consistent with global analyses.

Contribution

First lattice QCD calculation to fully decompose proton mass and momentum fractions with non-perturbative renormalization across multiple ensembles.

Findings

Quark energy contributes approximately 33% to proton mass.

Gluon field energy accounts for about 37% of the proton mass.

Trace anomaly contributes roughly 23% to the proton mass.

Abstract

We report results on the proton mass decomposition and also on 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 three volumes, and several pion masses including the physical pion mass. With fully non-perturbative renormalization (and universal normalization on both quark and gluon), we find that the quark energy and glue field energy contribute 33(4)(4)\% and 37(5)(4)\% respectively in the $\overline{MS}$ scheme at $\mu = 2$ GeV. A quarter of the trace anomaly gives a 23(1)(1)\% contribution to the proton mass based on the sum rule, given 9(2)(1)\% contribution from the $u, d,$ and $s$ quark scalar condensates. The $u,d,s$ and glue momentum fractions in the $\overline{MS}$ scheme are in good agreement with global analyses at $\mu = 2$ GeV.