We present a detailed lattice calculation of the unpolarized isovector quark PDF from the largemomentum effective theory approach. In this calculation, the quasi-PDF is defined by a spatial correlator that is free from mixing with operators of the same dimension, and is nonperturbatively renormalized in a regularization-independent momentum subtraction scheme. The renormalized quasi-PDF is then matched to the MS PDF at one-loop order in perturbative QCD. The lattice simulation is done using Gaussian-momentum-smeared source at Mπ = 310 MeV with the nucleon momentum Pz ∈ {1.7, 2.15, 2.6} GeV. Five source-sink separations have been used in our analysis to control the systematics associated with excited-state contamination. The systematic errors due to renormalization and perturbative matching are carefully studied. The final result is in reasonable agreement with the PDF from the latest phenomenological analyses.

Within the framework of large momentum effective theory (LaMET), generalized parton distributions (GPDs) can be extracted from lattice calculations of quasi-GPDs through a perturbative matching relation, up to power corrections that are suppressed by the hadron momentum. In this paper, we focus on isovector quark GPDs, including the unpolarized, longitudinally and transversely polarized cases, and present the one-loop matching that connects the quasi-GPDs renormalized in a regularization-independent momentum subtraction (RI/MOM) scheme to the GPDs in MS scheme. We find that the matching coefficient is independent of the momentum transfer squared. As a consequence, the matching for the quasi-GPD with zero skewness is the same as that for the quasi-PDF. Our results provide a crucial input for the determination of quark GPDs from lattice QCD using LaMET. *

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Within the factorization-assisted topologicalamplitude approach, we studied the 33 charmless B (s) → V V decays, where V stands for a light vector meson. According to the flavor flows, the amplitude of each process can be decomposed into eight different topologies. In contrast to the conventional flavor diagrammatic approach, we further factorize each topological amplitude into decay constant, form factors and unknown universal parameters. By χ 2 fitting 46 experimental observables, we extracted 10 theoretical parameters with χ 2 per degree of freedom around 2. Using the fitted parameters, we calculated the branching fractions, polarization fractions, CP asymmetries and relative phases between polarization amplitudes of each decay mode. The decay channels dominated by tree diagram have large branching fractions and large longitudinal polarization fraction. The branching fractions and longitudinal polarization fractions of color-suppressed decays become smaller. Current experimental data of large transverse polarization fractions in the penguin dominant decay channels can be explained by only one transverse amplitude of penguin annihilation diagram. Our predictions of the not yet measured channels can be tested in the ongoing LHCb experiment and the Belle-II experiment in the future.