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Pion Valence Quark Distribution at Physical Pion mass of $N_f=2+1+1$ Lattice QCD
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abstract
We present a state-of-the-art calculation of the unpolarized pion valence-quark distribution in the framework of large-momentum effective theory (LaMET) with improved handling of systematic errors as well as two-loop perturbative matching. We use lattice ensembles generated by the MILC collaboration at lattice spacing $a\approx 0.09$~fm, lattice volume $64^3\times 96$, $N_f=2+1+1$ flavors of highly-improved staggered quarks and a physical pion mass. The LaMET matrix elements are calculated with pions boosted to momentum $P_z\approx 1.72$~GeV with high-statistics of $O(10^6)$ measurements. We study the pion PDF in both hybrid-ratio and hybrid-regularization-independent momentum subtraction (hybrid-RI/MOM) schemes and also compare the systematic errors with and without the addition of leading-renormalon resummation (LRR) and renormalization-group resummation (RGR) in both the renormalization and lightcone matching. The final lightcone PDF results are presented in the modified minimal-subtraction scheme at renormalization scale $\mu=2.0$~GeV. We show that the $x$-dependent PDFs are compatible between the hybrid-ratio and hybrid-RI/MOM renormalization with the same improvements. We also show that systematics are greatly reduced by the simultaneous inclusion of RGR and LRR and that these methods are necessary if improved precision is to be reached with higher-order terms in renormalization and matching.
Forward citations
Cited by 6 Pith papers
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Resummation for Lattice QCD Calculation of Generalized Parton Distributions at Nonzero Skewness
A threshold factorization and resummation scheme for quasi-GPD matching in LaMET is derived and shown to be self-consistent on a GPD model.
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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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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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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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Effects of flavor-mixings on charged kaon and pion parton distribution functions
Vacuum-polarization flavor mixing in the U(3) NJL model produces small, mass-difference-driven shifts in charged pion and kaon valence PDFs that mildly improve agreement with data at 4 and 27 GeV².
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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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