[Submitted on 3 Aug 2022] (cross-list from hep-lat)
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🇩🇪
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 ~MeV at a lattice spacing ~fm and ~MeV at ~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 , and Mellin moments of the PDF. We reconstruct the Bjorken- 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.
- Comments:
- 25 pages, 29 figures, version published in PRD
- Subjects:
- High Energy Physics — Lattice (hep-lat); High Energy Physics — Experiment (hep-ex); High Energy Physics — Phenomenology (hep-ph); Nuclear Experiment (nucl-ex); Nuclear Theory (nucl-th)
- arXiv:
- 2208.02297 [pdf]