  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 $(5.76\mbox{
fm})^3$.
