Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA.
Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.
Phys Rev Lett. 2018 Nov 23;121(21):212001. doi: 10.1103/PhysRevLett.121.212001.
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 MS[over ¯] (modified minimal substraction) scheme at μ=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 MS[over ¯] scheme are in good agreement with global analyses at μ=2 GeV.
我们报告了质子质量分解的结果，以及相关的夸克和胶子动量分数的结果。这些结果是基于在具有三个格点间距和三个体积的 N_{f}=2+1 区域壁费米子组态的四个系综上的重叠价费米子得到的，包括物理介子质量在内的几个介子质量。通过完全非微扰重整化（以及夸克和胶子的通用归一化），我们发现在 MS[over ¯]（修正的最小减除）方案中，在 μ=2 GeV 时，夸克能量和胶子场能量分别贡献 32(4)(4)%和 36(5)(4)%。根据求和规则，trace anomaly 的四分之一对质子质量的贡献为 23(1)(1)%，其中 9(2)(1)%来自 u、d 和 s 夸克标量凝聚物。在 MS[over ¯]方案中，u、d、s 和胶子动量分数与 μ=2 GeV 时的全球分析结果一致。
