We study isovector unpolarized and helicity parton distribution functions (PDF) of proton within the framework of Large Momentum Effective Theory. We use a gauge ensemble, generated by the MILC collaboration, with a superfine lattice spacing of $0.042$~fm and a pion mass of $310$~MeV, enabling us to simultaneously reach sub-fermi spatial separations and larger nucleon momenta. We compare the spatial dependence of quasi-PDF matrix elements in different renormalization schemes with the corresponding results of the global fits, obtained using 1-loop perturbative matching. We present determinations of first four moments of the unpolarized and helicity PDFs of proton from the Ioffe-time dependence of the isovector matrix elements, obtained employing a ratio-based renormalization scheme.

中文翻译：

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超精细格上质子的等速向量parton分布函数

我们在大动量有效理论的框架内研究质子的等速矢量非极化和螺旋质子分布函数（PDF）。我们使用由MILC合作产生的轨距合奏，其晶格间距为$0.042$〜fm和pion质量 $310$〜MeV，使我们能够同时达到亚费米空间间隔和更大的核子动量。我们将使用不同的重归一化方案的准PDF矩阵元素的空间依赖性与使用1环扰动匹配获得的全局拟合的相应结果进行比较。我们根据等比例矩阵归一化方案从等矢量矩阵元素的Ioffe时间依赖性中确定质子的非极化和螺旋PDF的前四个矩。