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One of the great challenges of QCD is to determine the partonic structure ofthe nucleon from first principles. In this work, we provide such adetermination of the flavor non-singlet ($u-d$) unpolarized parton distributionfunction (PDF), utilizing the non-perturbative formulation of QCD on thelattice. We apply Radyushkin's pseudo-distribution approach to lattice resultsobtained using simulations with the light quark mass fixed to its physicalvalue; this is the first ever attempt for this approach directly at thephysical point. The extracted coordinate-space matrix elements are used to findthe relevant physical Ioffe time distributions from a matching procedure. Thefull Bjorken-$x$ dependence of PDFs is resolved using several reconstructionmethods to tackle the ill-conditioned inverse problem encountered when usingdiscrete lattice data. We consider both the valence distribution $q_v$ and thecombination with antiquarks $q_v+2\bar{q}$, related to, respectively, the realand imaginary part of extracted matrix elements. Good agreement is found withPDFs from global fits already within statistical uncertainties and it isfurther improved by quantifying several systematic effects. The resultspresented here are the first ever \emph{ab initio} determinations of PDFs fullyconsistent with global fits in the whole $x$-range. Thus, they pave the way toinvestigating a wider class of partonic distributions, such as e.g.\ singletPDFs and generalized parton distributions. Therefore, essential and yet missingfirst-principle insights can be achieved, complementing the rich experimentalprograms dedicated to the structure of the nucleon.

Flavor non-singlet parton distribution functions from lattice QCD at physical quark masses via the pseudo-distribution approach