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arXiv · 2208.02297

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

Xiang Gao·Andrew D. Hanlon·Nikhil Karthik·Swagato Mukherjee·Peter Petreczky·Philipp Scior·Shuzhe Shi·Sergey Syritsyn·Yong Zhao·Kai Zhou
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Abstract

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 $m_π=140$~MeV at a lattice spacing $a=0.076$~fm and $m_π=300$~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. We reconstruct the Bjorken-$x$ dependence of the NNLO PDF from real-space RGI ratios using a deep neural network (DNN) as well as from momentum-space matrix elements renormalized using a hybrid-scheme. All our results are in broad agreement with the results of global fits to the experimental data carried out by the xFitter and JAM collaborations.

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BibTeXRIS

Xiang Gao, Andrew D. Hanlon, Nikhil Karthik, Swagato Mukherjee, Peter Petreczky, Philipp Scior, Shuzhe Shi, Sergey Syritsyn, Yong Zhao, Kai Zhou. 2022-12-28. Continuum-extrapolated NNLO Valence PDF of Pion at the Physical Point. https://doi.org/10.1103/physrevd.106.114510

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