# The 39th International Symposium on Lattice Field Theory (Lattice 2022)

Aug 8 – 13, 2022
Hörsaalzentrum Poppelsdorf
Europe/Berlin timezone

## Lattice QCD Determination of the Bjorken-𝑥 Dependence of PDFs at Next-to-next-to-leading Order

Aug 10, 2022, 2:20 PM
20m
CP1-HSZ/Ground-0.010 - HS2 (CP1-HSZ)

450

Xiang Gao (ANL)

### Description

We report the first lattice QCD calculation of pion valence quark distribution with next-to-next-to-leading order perturbative matching correction, which is done using two fine lattices with spacings $a=0.04$ fm and $0.06$ fm and valence pion mass $m_\pi=300$ MeV, at boost momentum as large as $2.42$ GeV. As a crucial step to control the systematics, we renormalize the pion valence quasi distribution in the recently proposed hybrid scheme, which features a Wilson-line mass subtraction at large distances in coordinate space, and develop a procedure to match it to the $\overline{\rm MS}$ scheme. We demonstrate that the renormalization and the perturbative matching in Bjorken-$x$ space yield a reliable determination of the valence quark distribution for $x$ in range of 0.03 $\sim$ 0.80 with 5--20 % uncertainties.

### Primary authors

Andrew Hanlon (BNL) Xiang Gao (ANL) Peter Petreczky (BNL) Philipp Scior (BNL) Sergey Syritsyn (SBU) Swagato Mukherjee (BNL) Yong Zhao (ANL)