AI 中文总结
该研究基于2+1味格点QCD，利用高统计量数据计算核子的同位矢量动量分数、螺旋度矩和横度矩，其中前两者与唯象拟合结果一致，横度矩为新预测。
AI 中文摘要
本文利用由JLab/W&M/LANL/MIT/Marseille合作组生成的13套NME规范组态系综的高统计量数据，给出了核子的同位矢量动量分数⟨x⟩_{u-d}、螺旋度矩⟨x⟩_{Δu-Δd}和横度矩⟨x⟩_{δu-δd}的计算结果。与此前的格点计算相比，高统计量数据实现了对所有系统误差的更好控制。最难以控制的系统误差——激发态污染——通过研究结果随第一激发态质量间隙的三种估计值的变化来量化，该质量间隙由两点和三点关联函数得到。最终结果通过同时拟合外推得到，外推参数包括格距a、π介子和K介子质量M_π与M_K，以及有限体积参数M_πL。数据显示无显著的有限体积修正，且存在一定的格距和重整化因子依赖性。最大的系统误差来自可能剩余的激发态贡献。我们在2 GeV的overline{MS}方案下得到的最终结果为：⟨x⟩_{u-d}=0.154(10)(9)，⟨x⟩_{Δu-Δd}=0.177(10)(15)，⟨x⟩_{δu-δd}=0.197(12)(18)，其中第一个误差为整体统计不确定性，第二个为各类系统误差的平方和相加结果。动量分数和螺旋度矩的结果与唯象学全局拟合值一致，而横度矩为一项预测。
英文摘要
Results for the isovector momentum fraction, $\langle x \rangle_{u-d}$, helicity moment, $\langle x \rangle_{Δu-Δd}$, and the transversity moment, $\langle x\rangle_{δu-δd}$, of the nucleon are presented using high-statistics data on thirteen NME ensembles of gauge configurations generated by the JLab/W\&M/LANL/MIT/Marseille collaborations using $2+1$-flavors of dynamical Wilson-clover quarks. The much higher statistics facilitated better control over all systematics compared to our previous lattice calculation. The least controlled systematic---excited-state contamination---is quantified by studying the variation of the results as a function of three estimates of the mass gap of the first excited state, obtained from two- and three-point correlation functions. The final results are obtained using a simultaneous fit to extrapolate in the lattice spacing, $a$, pion and kaon masses, $M_π$ and $M_K$, and the finite volume parameter, $M_πL$. The data show no significant finite-volume correction, and some dependence on the lattice spacing and the renormalization factors. The largest systematic uncertainty is due to possible remaining excited states contributions. Our final results, in the $\overline{\rm MS}$ scheme at 2~GeV, are $\langle x \rangle_{u-d} = 0.154(10)(9)$, $\langle x \rangle_{Δu-Δd} = 0.177(10)(15)$ and $\langle x \rangle_{δu-δd} = 0.197(12)(18)$, where the first error is the overall statistical uncertainty and the second represents the various systematic uncertainties added in quadrature. Results for the momentum fraction and helicity moment are consistent with phenomenological global fit values, while the transversity moment is a prediction.
Comments41 pages, 13 figures
