Abstract

We present the first lattice results on isovector unpolarized and longitudinally polarized parton distribution functions (PDFs) at physical pion mass. 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 nonperturbatively in RI/MOM-scheme. However, the recent renormalized quasi-PDFs suffer from unphysical oscillations that alter the shape of the true distribution as a function of Bjorken-$x$. In this paper, we propose two possible solutions to overcome this problem, and demonstrate the efficacy of the methods on the 2+1+1-flavor lattice data at physical pion mass with lattice spacing 0.09~fm and volume $(5.76\mbox{ fm})^3$.

Highlights

  • We present the first lattice results on isovector unpolarized and longitudinally polarized parton distribution functions (PDFs) at physical pion mass

  • These distributions can be extracted through global analysis using multiple experiments by factorizing the hard-scattering cross sections into the PDFs and short-distance matrix elements that are calculable in perturbation theory

  • Progress has been made in polarized PDFs using data from RHIC at Brookhaven National Lab and the COMPASS experiment at CERN; further progress would be made at the proposed electron-ion collider (EIC)

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Summary

Introduction

We present the first lattice results on isovector unpolarized and longitudinally polarized parton distribution functions (PDFs) at physical pion mass. The quasi-PDF nucleon matrix elements are renormalized nonperturbatively in the RI/MOM-scheme.

Results
Conclusion
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