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Unpolarized proton PDF at NNLO from lattice QCD with physical quark masses
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abstract
We present a lattice QCD calculation of the unpolarized isovector quark parton distribution function (PDF) of the proton utilizing a perturbative matching at next-to-next-to-leading-order (NNLO). The calculations are carried out using a single ensemble of gauge configurations generated with $N_f = 2 + 1$ highly-improved staggered quarks with physical masses and a lattice spacing of $a = 0.076$ fm. We use one iteration of hypercubic smearing on these gauge configurations, and the resulting smeared configurations are then used for all aspects of the subsequent calculation. For the valence quarks, we use the Wilson-clover action with physical quark masses. We consider several methods for extracting information on the PDF. We first extract the lowest four Mellin moments using the leading-twist operator product expansion approximation. Then, we determine the $x$ dependence of the PDF through a deep neural network within the pseudo-PDF approach and additionally through the framework of large-momentum effective theory utilizing a hybrid renormalization scheme. This is the first application of the NNLO matching coefficients for the nucleon directly at the physical point.
Forward citations
Cited by 7 Pith papers
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Light Cone Distribution Amplitude for the $\Lambda$ Baryon from Lattice QCD
The first lattice QCD extraction of the Lambda baryon's light-cone distribution amplitude via LaMET yields a momentum-fraction distribution peaked at small light-quark momenta.
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The nucleon unpolarized generalized form factors and Mellin moments up to fourth order
First lattice-QCD extraction of nucleon unpolarized Mellin moments through fourth order at physical pion mass, with GFF Q^{2} dependence and a reconstructed isovector valence PDF.
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A Unified Neural-Network Framework for Nucleon Imaging from Numerical Simulations of QCD
One neural network simultaneously fits LaMET and short-distance-expansion lattice data to reconstruct light-cone PDFs and zero-skewness GPDs of the nucleon.
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Gradient flow for parton distribution functions: first application to the pion
Pion PDF moment ratios up to <x^5> were extracted from lattice QCD with gradient flow and agree with phenomenological fits.
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Ill-Posedness in Limited Discrete Fourier Inversion and Regularization for Quasi Distributions in LaMET
Tikhonov regularization with L-curve parameter choice stabilizes the ill-conditioned limited inverse Fourier transform in LaMET and recovers pion quasi distribution amplitudes consistent with physics-driven lambda-ext...
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A simple non-parametric reconstruction of parton distributions from limited Fourier information
A fixed-hyperparameter Gaussian-process prior recovers parton distributions from limited Ioffe-time data and yields more realistic small-x uncertainties than simple parametric fits.
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Mapping Parton Distributions of Hadrons with Lattice QCD
A review of lattice QCD methods and results for x-dependent parton distribution functions and generalized parton distributions of hadrons.
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