标题： 具有 $N_f=2+1$ 种 $\mathcal{O}(a)$ 改进的威尔逊费米子的同位旋核矩阵元的改进分析 显示英文标题

标题： Improved analysis of isovector nucleon matrix elements with $N_f=2+1$ flavors of $\mathcal{O}(a)$ improved Wilson fermions

摘要： 我们给出了对同位旋电荷$g_A^{u-d}$、$g_S^{u-d}$和$g_T^{u-d}$以及同位旋 twist-2 前向矩阵元$\langle x\rangle_{u-d}$、$\langle x\rangle_{\Delta u-\Delta d}$和$\langle x\rangle_{\delta u-\delta d}$的确定结果的更新，这些结果是在由协调格点模拟（CLS）合作项目生成的$N_\mathrm{f}=2+1$格点规范场配置上计算得到的。 通过加入物理 pion 质量和精细晶格间距的集合、接近物理 pion 质量和非常精细晶格间距的集合、以及非常大的物理晶格体积的集合，我们显著扩展了参数空间的覆盖范围，从而能够很好地控制到物理点的外推。 另一个重大改进是由于源-汇分离范围的扩展，这使我们能够对累积关联比进行双态拟合，从而大大提高了对激发态效应的控制水平。 利用基于赤池信息准则（Akaike Information Criterion）的模型平均方法，将来自手征、连续极限和无限体积外推的系统不确定性纳入考虑之中。 我们的最终结果在物理点上为 $g_A^{u-d} = 1.254(19)_\mathrm{stat}(15)_\mathrm{sys}[24]_\mathrm{total}$, $g_S^{u-d} = 1.203(77)_\mathrm{stat}(81)_\mathrm{sys}[112]_\mathrm{total}$, $g_T^{u-d} = 0.993(15)_\mathrm{stat}(05)_\mathrm{sys}[16]_\mathrm{total}$, $\langle x\rangle_{u-d} = 0.153(15)_\mathrm{stat}(10)_\mathrm{sys}[17]_\mathrm{total}$, $\langle x\rangle_{\Delta u - \Delta d} = 0.207(15)_\mathrm{stat}(06)_\mathrm{sys}[16]_\mathrm{total}$, 和 $\langle x\rangle_{\delta u - \delta d} = 0.195(17)_\mathrm{stat}(15)_\mathrm{sys}[23]_\mathrm{total}$。 虽然我们得到的同位旋电荷的结果与FLAG 21的平均值非常一致，但我们注意到我们对张量电荷 $g_T^{u-d}$ 的误差要小得多。 显示英文摘要

摘要： We present an update of our determination of the isovector charges $g_A^{u-d}$, $g_S^{u-d}$ and $g_T^{u-d}$, and the isovector twist-2 forward matrix elements $\langle x\rangle_{u-d}$, $\langle x\rangle_{\Delta u-\Delta d}$ and $\langle x\rangle_{\delta u-\delta d}$ on the $N_\mathrm{f}=2+1$ gauge ensembles generated by the Coordinated Lattice Simulations (CLS) effort. We have significantly extended our coverage of the parameter space by adding ensembles at the physical pion mass and fine lattice spacing, at nearly-physical pion masses and very fine lattice spacings, and at very large physical lattice volumes, enabling a well-controlled extrapolation to the physical point. Another major improvement is achieved owing to the extended range of source-sink separations, which allows us to perform two-state fits to summed correlator ratios, leading to a much higher level of control over excited-state effects. Systematic uncertainties from the chiral, continuum and infinite-volume extrapolations are incorporated via model averages based on the Akaike Information Criterion. Our final results at the physical point are $g_A^{u-d} = 1.254(19)_\mathrm{stat}(15)_\mathrm{sys}[24]_\mathrm{total}$, $g_S^{u-d} = 1.203(77)_\mathrm{stat}(81)_\mathrm{sys}[112]_\mathrm{total}$, $g_T^{u-d} = 0.993(15)_\mathrm{stat}(05)_\mathrm{sys}[16]_\mathrm{total}$, $\langle x\rangle_{u-d} = 0.153(15)_\mathrm{stat}(10)_\mathrm{sys}[17]_\mathrm{total}$, $\langle x\rangle_{\Delta u - \Delta d} = 0.207(15)_\mathrm{stat}(06)_\mathrm{sys}[16]_\mathrm{total}$, and $\langle x\rangle_{\delta u - \delta d} = 0.195(17)_\mathrm{stat}(15)_\mathrm{sys}[23]_\mathrm{total}$. While our results for the isovector charges are in excellent agreement with the FLAG\,21 averages, we note that our error for the tensor charge $g_T^{u-d}$ is considerably smaller.