Abstract
We present the first lattice-QCD calculation of the isovector polarized parton distribution functions (both helicity and transversity) using the large-momentum effective field theory (LaMET) approach for direct Bjorken-x dependence. We first review the detailed steps of the procedure in the unpolarized case, then generalize to the helicity and transversity cases. We also derive a new mass-correction formulation for all three cases. We then compare the effects of each finite-momentum correction using lattice data calculated at Mπ≈310 MeV. Finally, we discuss the implications of these results for the poorly known antiquark structure and predict the sea-flavor asymmetry in the transversely polarized nucleon.
Highlights
Parton distribution functions (PDFs) provide a universal description of the proton’s constituents
Those lightcone correlators become local operators in Euclidean space and lead to unphysical results. This problem can be avoided by working with moments of parton distributions, which correspond to matrix elements of local operators, provided all the moments can be computed to recover the whole PDF
We report the results of a lattice-QCD calculation using clover valence fermions on an ensemble of gauge configurations with lattice spacing a = 0.12 fm, box size L ≈ 3 fm and pion mass Mπ ≈ 310 MeV with Nf = 2 + 1 + 1 flavors of highly improved staggered quarks (HISQ) [29] generated by MILC Collaboration [30]
Summary
Parton distribution functions (PDFs) provide a universal description of the proton’s constituents (quarks, antiquarks and gluons). The parton distributions are related to nucleon matrix elements of quark correlators defined on a lightcone in Minkowski space Those lightcone correlators become local operators in Euclidean space and lead to unphysical results (see more detailed discussion ). In principle, this problem can be avoided by working with moments of parton distributions, which correspond to matrix elements of local operators, provided all the moments can be computed to recover the whole PDF. There have been many follow-up calculations to determine the one-loop corrections needed to connect finite-momentum quasi-distributions to IMF/lightcone distributions for nonsinglet leading-twist PDFs [16], generalized parton distributions (GPDs) [17] and transversity GPDs [18] in the continuum. The details of the finite-momentum corrections are given in the Appendices
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