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 $N_f=2+1$ domain wall fermion configurations with three lattice spacings and three volumes, and several pion masses including the physical pion mass. With fully nonperturbative renormalization (and universal normalization on both quark and gluon), we find that the quark energy and glue field energy contribute 32(4)(4)% and 36(5)(4)% respectively in the $\overline{\mathrm{MS}}$ (modified minimal substraction) scheme at $\mu =2\mathrm{GeV}$. 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 $\overline{\mathrm{MS}}$ scheme are in good agreement with global analyses at $\mu =2\mathrm{GeV}$.

• Received 4 September 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.212001

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Published by the American Physical Society