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 quasidistributions at proton momenta $P_z\in \{2.2,2.6,3.0\}\mathrm{GeV}$ on the lattice and match them systematically to the physical parton distribution using the large-momentum effective theory. We reach an unprecedented precision through high statistics in simulations, large-momentum proton matrix elements, and control of excited-state contamination. The resulting distribution with combined statistical and systematic errors is in agreement with the latest phenomenological analysis of the spin-dependent experimental data, in particular, $\mathrm{\Delta }\overline{u}(x)>\mathrm{\Delta }\overline{d}(x)$.

We present a detailed lattice QCD study of the unpolarized isovector quark parton distribution function (PDF) using a large-momentum effective theory framework. We choose a quasi-PDF defined by a spatial correlator which is free from mixing with other operators of the same dimension. In the lattice simulation, we use a Gaussian-momentum-smeared source at $M_{\pi }=356\mathrm{MeV}$ and $P_z\in \{1.8,2.3\}\mathrm{GeV}$. To control the systematics associated with the excited states, we explore five different source-sink separations. The nonperturbative renormalization is conducted in a regularization-independent momentum subtraction scheme, and the matching between the renormalized quasi-PDF and $\overline{\mathrm{MS}}$ PDF is calculated based on perturbative QCD up to one-loop order. Systematic errors due to renormalization and perturbative matching are also analyzed in detail. Our results for light-cone PDF are in reasonable agreement with the latest phenomenological analysis.

We present a state-of-the-art lattice QCD calculation of the pion and kaon light-cone distribution amplitudes (DAs) using large-momentum effective theory. The calculation is done at three lattice spacings $a\approx \{0.06,0.09,0.12\}\mathrm{fm}$ and physical pion and kaon masses, with the meson momenta $P_z=\{1.29,1.72,2.15\}\mathrm{GeV}$. The result is nonperturbatively renormalized in a recently proposed hybrid scheme with self-renormalization, and extrapolated reliably to the continuum as well as the infinite momentum limit. We find a significant deviation of the pion and kaon DAs from the asymptotic form, and a large $SU(3)$ flavor breaking effect in the kaon DA.

The transverse-momentum-dependent (TMD) soft function is a key ingredient in QCD factorization of Drell-Yan and other processes with relatively small transverse momentum. We present a lattice QCD study of this function at moderately large rapidity on a $2+1$ flavor CLS dynamic ensemble with $a=0.098\mathrm{fm}$. We extract the rapidity-independent (or intrinsic) part of the soft function through a large-momentum-transfer pseudoscalar meson form factor and its quasi-TMD wave function using leading-order factorization in large-momentum effective theory. We also investigate the rapidity-dependent part of the soft function—the Collins-Soper evolution kernel—based on the large-momentum evolution of the quasi-TMD wave function.

We study isovector unpolarized and helicity parton distribution functions (PDF) of the 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 one-loop perturbative matching. We present determinations of the first four moments of the unpolarized and helicity PDFs of proton from the Ioffe-time dependence of the isovector matrix elements, obtained by employing a ratio-based renormalization scheme.