标题： 探测介子部分子分布函数的高阶矩 显示英文标题

标题： Probing higher moments of pion parton distribution functions

摘要： 我们首次对参考文献[1]中提出的方法进行了数值研究，该方法利用梯度流从格点QCD中获得PDF更高阶矩的精确测定，从而避免与低维算符的幂发散混合。我们将此方法应用于使用四个稳定威尔逊费米子系综获得介子的等效矢量PDF的矩，其中$m_{\pi}\simeq 411$ MeV和格点间距为$a \simeq 0.064, 0.077, 0.094$，以及$0.12$ fm。我们展示了三点函数比值随流时间变化的初步结果，这些比值可用于提取$\left\langle x^2 \right\rangle/\left\langle x \right\rangle$和$\left\langle x^3 \right\rangle/\left\langle x \right\rangle$。我们发现，与需要提升且最多只能达到$\left\langle x^3 \right\rangle$矩的经典方法相比，此方法可以显著提高精度。 显示英文摘要

摘要： We present the first numerical investigation of the method proposed in Ref. [1] to utilize gradient flow to obtain precise determinations of higher moments of PDFs from lattice QCD, circumventing power divergent mixing with lower dimensional operators. We apply this method to obtain moments of the isovector PDF of the pion using four Stabilized Wilson Fermion ensembles with $m_{\pi}\simeq 411$ MeV and lattice spacings $a \simeq 0.064, 0.077, 0.094$, and $0.12$ fm. We present preliminary results of ratios of three-point functions as a function of flow time, which can be used to extract the ratios $\left\langle x^2 \right\rangle/\left\langle x \right\rangle$ and $\left\langle x^3 \right\rangle/\left\langle x \right\rangle$. We find that a significantly higher precision can be achieved with this method compared to the canonical approach, which requires boosting and cannot reach higher than the $\left\langle x^3 \right\rangle$ moment.