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  1. We study and demonstrate the ground-state extrapolation of the unpolarized and polarized nucleon quark quasi-PDF matrix elements in a highly boosted hadron frame on the lattice. The calculation is done using the Wilson clover quark on a MILC’s dynamical Nf = 2+1+1 highly improved staggered quarks (HISQ) ensemble with one step hypercubic smearing, and with the lattice spacing a∼0.09 fm and pion mass 310 MeV. Applying the Gaussian momentum-smeared quark sources and comparing various fits in 1-, 2-, and 3-state fitting models, we show that excited state contributions can be under control in the lattice calculation of the nucleon quark quasi-PDF matrix elements.
  2. We present a state-of-the-art calculation of the isovector quark helicity Bjorken-$x$ distribution in the proton using lattice-QCD ensembles at the physical pion mass. We compute quasi-distributions at proton momenta $P_z \in \{2.2, 2.6, 3.0\}$~GeV on the lattice, and match them systematically to the physical parton distribution using large-momentum effective theory (LaMET). We reach an unprecedented precision through high statistics in simulations, large-momentum proton matrix elements, and control of excited-state contamination. The resulting distribution is in agreement within $2\sigma$ with the latest phenomenological analysis of the spin-dependent experimental data; in particular, $\Delta \bar{u}(x)>\Delta \bar{d}(x)$.