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2022

Continuum-extrapolated NNLO Valence PDF of Pion at the Physical Point

Gao, Xiang, Hanlon, Andrew D., Karthik, Nikhil et al.

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We present lattice QCD calculations of valence parton distribution function (PDF) of pion employing next-to-next-leading-order (NNLO) perturbative QCD matching.

Our calculations are based on three gauge ensembles of 2+1 flavor highly improved staggered quarks and Wilson--Clover valance quarks, corresponding to pion mass $m_\pi=140$~MeV at a lattice spacing $a=0.076$~fm and $m_\pi=300$~MeV at $a=0.04, 0.06$~fm.
This enables us to present, for the first time, continuum-extrapolated lattice QCD results for NNLO valence PDF of the pion at the physical point.
Applying leading-twist expansion for renormalization group invariant (RGI) ratios of bi-local pion matrix elements with NNLO Wilson coefficients we extract $2^{\mathrm{nd}}$, $4^{\mathrm{th}}$ and $6^{\mathrm{th}}$ Mellin moments of the PDF.

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