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The Unpolarized Proton PDF at NNLO from Lattice QCD with Physical Quark Masses

Xiang GaoAndrew D. HanlonJack Holligan ...+4 Yong Zhao
Dec 2022
摘要
We present a lattice QCD calculation of the unpolarized isovector quarkparton distribution function (PDF) of the proton utilizing a perturbativematching at next-to-next-leading-order (NNLO). The calculations are carried outusing a single ensemble of gauge configurations generated with $N_f = 2 + 1$highly improved staggered quarks with physical masses and a lattice spacing of$a = 0.076$ fm. We use one iteration of hypercubic smearing on these gaugeconfigurations, and the resulting smeared configurations are then used for allaspects of the subsequent calculation. For the valence quarks, we use theWilson-clover action with physical quark masses. We consider several methodsfor extracting information on the PDF. We first extract the lowest four Mellinmoments using the leading-twist operator product expansion approximation. Then,we determine the $x$ dependence of the PDF through a deep neural network withinthe pseudo-PDF approach and additionally through the framework oflarge-momentum effective theory utilizing a hybrid renormalization scheme. Thisis the first application of the NNLO matching coefficients for the nucleondirectly at the physical point.
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