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arXiv 2402.03024hep-lathep-phnucl-th
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改进的 $N_f=2+1$ 味 $\nmathcal{O}(a)$ 改进 Wilson 费米子等矢量核子矩阵元分析

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

Dalibor Djukanovic, Georg von Hippel, Harvey B. Meyer, Konstantin Ottnad, Hartmut Wittig

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20 pages, 11 figures
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AI总结：

本研究在 CLS 系综上改进等矢量核子矩阵元的计算，通过扩展参数空间和双态拟合控制激发态效应，得到与 FLAG 21 一致且张量电荷误差更小的精确结果。

摘要：

我们展示了在 Coordinated Lattice Simulations (CLS) 合作组生成的 $N_\mathrm{f}=2+1$ 规范系综上，对等矢量电荷 $g_A^{u-d}$、$g_S^{u-d}$ 和 $g_T^{u-d}$，以及等矢量 twist-2 前向矩阵元 $\langle x\rangle_{u-d}$、$\langle x\rangle_{\Delta u-\Delta d}$ 和 $\langle x\rangle_{\delta u-\delta d}$ 的测定更新。我们通过增加物理 pion 质量和精细格点间距的系综、近物理 pion 质量和极精细格点间距的系综，以及非常大的物理格点体积的系综，显著扩展了参数空间的覆盖范围，从而能够对物理点进行良好控制的 extrapolation。另一项重大改进源于源-汇分离范围的扩展，这使得我们能够对求和关联比进行双态拟合，从而对激发态效应实现更高水平的控制。来自手征、连续和无限体积 extrapolation 的系统不确定性通过基于 Akaike 信息准则的模型平均纳入。我们在物理点的最终结果为 $g_A^{u-d} = 1.254(19)_\mathrm{stat}(15)_\mathrm{sys}[24]_\mathrm{total}$，$g_S^{u-d} = 1.203(77)_\mathrm{stat}(81)_\mathrm{sys}[112]_\mathrm{total}$，$g_T^{u-d} = 0.993(15)_\mathrm{stat}(05)_\mathrm{sys}[16]_\mathrm{total}$，$\langle x\rangle_{u-d} = 0.153(15)_\mathrm{stat}(10)_\mathrm{sys}[17]_\mathrm{total}$，$\langle x\rangle_{\Delta u - \Delta d} = 0.207(15)_\mathrm{stat}(06)_\mathrm{sys}[16]_\mathrm{total}$，以及 $\langle x\rangle_{\delta u - \delta d} = 0.195(17)_\mathrm{stat}(15)_\mathrm{sys}[23]_\mathrm{total}$。虽然我们的等矢量电荷结果与 FLAG\\,21 平均值非常一致，但我们注意到我们的张量电荷 $g_T^{u-d}$ 的误差要小得多。

英文摘要：

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 $\langle x\rangle_{u-d}$, $\langle x\rangle_{Δu-Δd}$ and $\langle x\rangle_{δu-δd}$ 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 $g_A^{u-d} = 1.254(19)_\mathrm{stat}(15)_\mathrm{sys}[24]_\mathrm{total}$, $g_S^{u-d} = 1.203(77)_\mathrm{stat}(81)_\mathrm{sys}[112]_\mathrm{total}$, $g_T^{u-d} = 0.993(15)_\mathrm{stat}(05)_\mathrm{sys}[16]_\mathrm{total}$, $\langle x\rangle_{u-d} = 0.153(15)_\mathrm{stat}(10)_\mathrm{sys}[17]_\mathrm{total}$, $\langle x\rangle_{Δu - Δd} = 0.207(15)_\mathrm{stat}(06)_\mathrm{sys}[16]_\mathrm{total}$, and $\langle x\rangle_{δu - δd} = 0.195(17)_\mathrm{stat}(15)_\mathrm{sys}[23]_\mathrm{total}$. 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.

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