Flavor nonsinglet parton distribution functions from lattice QCD at physical quark masses via the pseudodistribution approach

One of the great challenges of QCD is to determine the partonic structure of the nucleon from first principles. In this work, we provide such a determination of the flavor nonsinglet (u - d) unpolarized parton distribution function (PDF), utilizing the nonperturbative formulation of QCD on the lattice. We apply Radyushkin's pseudodistribution approach to lattice results obtained using simulations with the light quark mass fixed to its physical value; this is the first ever attempt for this approach directly at the physical point. The extracted coordinate-space matrix elements are used to find the relevant physical Ioffe time distributions from a matching procedure. The full Bjorken-x dependence of PDFs is resolved using several reconstruction methods to tackle the ill-conditioned inverse problem encountered when using discrete lattice data. We consider both the valence distribution q(v) and the combination with antiquarks q(v) + 2 (q) over bar, related to, respectively, the real and imaginary part of extracted matrix elements. Good agreement is found with PDFs from global fits already within statistical uncertainties and it is further improved by quantifying several systematic effects. The results presented here are the first ever ab initio determinations of PDFs fully consistent with global fits in the whole x range. Thus, they pave the way to investigating a wider class of partonic distributions, such as e.g., singlet PDFs and generalized parton distributions. Therefore, essential and yet missing first-principle insights can be achieved, complementing the rich experimental programs dedicated to the structure of the nucleon.

Automated summary

This study provides a determination of the flavor nonsinglet (u - d) unpolarized parton distribution function using the nonperturbative formulation of QCD on the lattice, making the first attempt at using Radyushkin's pseudodistribution approach directly at the physical point. Extracted coordinate-space matrix elements are used to find the relevant physical Ioffe time distributions, resolving the full Bjorken-x dependence of PDFs with various reconstruction methods to handle ill-conditioned inverse problems encountered with discrete lattice data.