Lattice QCD Determination of the Bjorken-$x$ Dependence of Parton Distribution Functions at Next-to-next-to-leading Order

Abstract

We report the first lattice QCD calculation of pion valence quark distribution with next-to-next-to-leading order perturbative matching correction, which is done using two fine lattices with spacings $a=0.04$ fm and $0.06$ fm and valence pion mass $m_{\pi }=300$ MeV, at boost momentum as large as $2.42$ GeV. As a crucial step to control the systematics, we renormalize the pion valence quasi distribution in the recently proposed hybrid scheme, which features a Wilson-line mass subtraction at large distances in coordinate space, and develop a procedure to match it to the $\overline{\mathrm{MS}}$ scheme. We demonstrate that the renormalization and the perturbative matching in Bjorken-$x$ space yield a reliable determination of the valence quark distribution for $0.03\lesssim x\lesssim 0.80$ with 5-20\% uncertainties.

arXiv comment4 pages, 4 figures and appendix

References in corpus (58)

• The equation of state in (2+1)-flavor QCD
• Parton Physics on Euclidean Lattice
• Flavor Symmetry and the Static Potential with Hypercubic Blocking
• Highly Improved Staggered Quarks on the Lattice, with Applications to Charm Physics
• Heavy Quark Effective Theory beyond Perturbation Theory: Renormalons, the Pole Mass and the Residual Mass Term
• Quasi-PDFs, momentum distributions and pseudo-PDFs
• Parton distributions and lattice QCD calculations: a community white paper
• Large-Momentum Effective Theory
• Exploring hadrons' partonic structure using ab initio lattice QCD calculations
• Soft-Gluon Resummation and the Valence Parton Distribution Function of the Pion
• Extracting Parton Distribution Functions from Lattice QCD Calculations
• Nucleon structure functions from lattice operator product expansion
• Exclusive processes in position space and the pion distribution amplitude
• Factorization Theorem Relating Euclidean and Light-Cone Parton Distributions
• One-Loop Matching for Parton Distributions: Non-Singlet Case
• Origin of Difference between $\overline{d}$ and $\overline{u}$ Partons in the Nucleon
• A complete non-perturbative renormalization prescription for quasi-PDFs
• Perturbative Renormalization of quasi-PDFs
• On the Renormalizability of Quasi Parton Distribution Functions
• Renormalization in Large Momentum Effective Theory of Parton Physics
• Deep-inelastic scattering and the operator product expansion in lattice QCD
• Pion Distribution Amplitude from Lattice QCD
• Pion Valence Quark Distribution from Matrix Element Calculated in Lattice QCD
• Nonperturbative renormalization of nonlocal quark bilinears for quasi-PDFs on the lattice using an auxiliary field
• Parton Distribution Function with Non-perturbative Renormalization from Lattice QCD
• Pion Valence Structure from Ioffe Time Pseudo-Distributions
• First direct lattice-QCD calculation of the $x$-dependence of the pion parton distribution function
• Valence parton distribution function of pion from fine lattice
• Polyakov loop in 2+1 flavor QCD from low to high temperatures
• Matching the Quasi Parton Distribution in a Momentum Subtraction Scheme
• Parton Distribution Functions of the Charged Pion Within The xFitter Framework
• Valence parton distribution of pion from lattice QCD: Approaching continuum
• Power corrections and renormalons in parton quasi-distributions
• More On Large-Momentum Effective Theory Approach to Parton Physics
• A Hybrid Renormalization Scheme for Quasi Light-Front Correlations in Large-Momentum Effective Theory
• Pion valence quark distribution from current-current correlation in lattice QCD
• Systematic uncertainties in parton distribution functions from lattice QCD simulations at the physical point
• Equation of State in 2+1 Flavor QCD at High Temperatures
• The static potential: lattice versus perturbation theory in a renormalon-based approach
• Valence-Quark Distribution of the Kaon and Pion from Lattice QCD
• Color screening in (2+1)-flavor QCD
• Quark Pseudo-Distributions at Short Distances
• Self-Renormalization of Quasi-Light-Front Correlators on the Lattice
• Perturbative expansion of the energy of static sources at large orders in four-dimensional SU(3) gauge theory
• Compelling evidence of renormalons in QCD from high order perturbative expansions
• Isovector parton distribution functions of the proton on a superfine lattice
• Model-independent determination of the gluon condensate in four-dimensional SU(3) gauge theory
• Extraction of Next-to-Next-to-Leading-Order PDFs from Lattice QCD Calculations
• The moment $⟨x{⟩}_{u-d}$ of the nucleon from $N_f=2$ lattice QCD down to nearly physical quark masses
• Distribution Amplitudes of $K^{\ast }$ and $\varphi$ at Physical Pion Mass from Lattice QCD
• Perturbative expansion of the plaquette to $\mathcal{O}({\alpha }^{35})$ in four-dimensional SU(3) gauge theory
• Lattice continuum-limit study of nucleon quasi-PDFs
• Origin and Resummation of Threshold Logarithms in the Lattice QCD Calculations of PDFs
• Next-to-next-to-leading order corrections to quark Quasi parton distribution functions
• Calculation and Interpretation of Hadron Correlation Functions in Lattice QCD
• Improvement, generalization, and scheme conversion of Wilson-line operators on the lattice in the auxiliary field approach
• Renormalization of parton quasi-distributions beyond the leading order: spacelike vs. timelike
• Strong coupling constant from moments of quarkonium correlators revisited

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• Large-Momentum Effective Theory's Asymptotic Extrapolation vs the Inverse Problem
• Searching for $a_0(980)$-meson parton distribution function
• Renormalon effect of quasi-PDF in gradient flow formalism
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• Lattice QCD Benchmark of Proton Helicity and Flavor-Dependent Unpolarized Transverse Momentum-Dependent Parton Distribution Functions at Physical Quark Masses