Abstract
Recently, there have been rapid developments in lattice-QCD calculations of proton structure, especially in the parton distribution functions (PDFs). We overcame a longstanding obstacle and for the first time in lattice-QCD are able to directly calculate the Bjorken-x dependence of the quark, helicity and transversity distributions. The PDFs are obtained using the large-momentum effective field theory (LaMET) framework where the full Bjorken-x dependence of finite-momentum PDFs, called “quasi-PDFs”, can be calculated on the lattice. The quasi-PDF nucleon matrix elements are renormalized non-perturbatively in RI/MOM-scheme. Following a nonperturbative renormalization of the parton quasi-distribution in a regularization-independent momentum-subtraction scheme, we establish its matching to the $ \overline {{\rm{MS}}} $ PDF and calculate the non-singlet matching coefficient at next-to-leading order in perturbation theory. In this proceeding, I will show the progress that has been made in recent years, highlighting the latest state-of-the art PDF calculations at the physical pion mass. Future impacts on the large-x global PDF fits are also discussed.
Highlights
Parton distribution functions (PDFs) are important quantities describing the probability densities of quarks and gluons within hadrons
Lattice-quantum chromodynamics (QCD) studies based on the operator product expansion (OPE) could only access the lower moments of the PDF.A similar situation occurs in lattice calculations of other parton observables, such as the distribution amplitudes (DAs) and generalized parton distributions (GPDs)
We show the impact on the PDF uncertainties in uand dat large-x in the upper plots, with the corresponding comparison for ∆uand ∆din the lower plots
Summary
Parton distribution functions (PDFs) are important quantities describing the probability densities of quarks and gluons within hadrons. There has been a promising proposal, large-momentum effective theory (LaMET), [1] wherein the PDFs and other parton observables can be directly extracted from the lattice by calculating the matrix elements of certain static operators in a boosted hadron state. There have been other proposals to calculate the PDFs in lattice QCD [19,20,21,22,23,24,25,26,27] which are subject to their own systematics; they can be complementary to each other as well as to the LaMET approach In this proceeding, I report on state-of-the-art lattice calculations of the unpolarized, longitudinally and transversely polarized isovector quark distributions at physical pion mass using the LaMET method. It signals a promising trend that the precision of lattice calculations is approaching the precision of phenomenological studies with increasing computing resources
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