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

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 $m_{\pi }=140$~MeV at a lattice spacing $a=0.076$~fm and $m_{\pi }=300$~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.

arXiv comment25 pages, 29 figures, version published in PRD

References in corpus (84)

• Parton Physics on Euclidean Lattice
• Solving Lattice QCD systems of equations using mixed precision solvers on GPUs
• Highly Improved Staggered Quarks on the Lattice, with Applications to Charm Physics
• Quasi-PDFs, momentum distributions and pseudo-PDFs
• Large-Momentum Effective Theory
• Exploring hadrons' partonic structure using ab initio lattice QCD calculations
• Nucleon Helicity and Transversity Parton Distributions from Lattice QCD
• Extracting Parton Distribution Functions from Lattice QCD Calculations
• Novel quark smearing for hadrons with high momenta in lattice QCD
• 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
• Pion and Kaon Structure at the Electron-Ion Collider
• Origin of Difference between $\overline{d}$ and $\overline{u}$ Partons in the Nucleon
• A complete non-perturbative renormalization prescription for quasi-PDFs
• Parton distributions and lattice QCD calculations: toward 3D structure
• 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
• Reconstruction of light-cone parton distribution functions from lattice QCD simulations at the physical point
• 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
• Covariant approximation averaging
• Pion Valence Structure from Ioffe Time Pseudo-Distributions
• Transversity parton distribution functions from lattice QCD
• First direct lattice-QCD calculation of the $x$-dependence of the pion parton distribution function
• Valence parton distribution function of pion from fine lattice
• Matching the Quasi Parton Distribution in a Momentum Subtraction Scheme
• Parton Distribution Functions of the Charged Pion Within The xFitter Framework
• Meson Screening Masses in (2+1)-Flavor QCD
• Valence parton distribution of pion from lattice QCD: Approaching continuum
• Proton Isovector Helicity Distribution on the Lattice at Physical Pion Mass
• Reconstructing parton distribution functions from Ioffe time data: from Bayesian methods to Neural Networks
• Moments of Ioffe time parton distribution functions from non-local matrix elements
• 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
• Adaptive Multigrid Algorithm for Lattice QCD
• Gluon Quasi-PDF From Lattice QCD
• Parton Distribution Functions from Ioffe time pseudo-distributions
• Parton Distribution Functions from Ioffe Time Pseudodistributions from Lattice Calculations: Approaching the Physical Point
• Unpolarized isovector quark distribution function from Lattice QCD: A systematic analysis of renormalization and matching
• Color screening in (2+1)-flavor QCD
• Nucleon Tomography and Generalized Parton Distribution at Physical Pion Mass from Lattice QCD
• The Universal Approximation Property
• Quark Pseudo-Distributions at Short Distances
• Self-Renormalization of Quasi-Light-Front Correlators on the Lattice
• Isovector parton distribution functions of the proton on a superfine lattice
• Extraction of Next-to-Next-to-Leading-Order PDFs from Lattice QCD Calculations
• Lattice QCD Determination of the Bjorken-$x$ Dependence of Parton Distribution Functions at Next-to-next-to-leading Order
• Nucleon Helicity Generalized Parton Distribution at Physical Pion Mass from Lattice QCD
• Heavy quark potential in quark-gluon Plasma: Deep neural network meets lattice quantum chromodynamics
• Confronting lattice parton distributions with global QCD analysis
• Gluon Parton Distribution of the Pion from Lattice QCD
• Flavor non-singlet parton distribution functions from lattice QCD at physical quark masses via the pseudo-distribution approach
• Distribution Amplitudes of $K^{\ast }$ and $\varphi$ at Physical Pion Mass from Lattice QCD
• 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
• New insights on proton structure from lattice QCD: the twist-3 parton distribution function $g_T(x)$
• Finite-volume effects due to spatially non-local operators
• Neural-network analysis of Parton Distribution Functions from Ioffe-time pseudodistributions
• $⟨x⟩$ and $⟨x^2⟩$ of the pion PDF from Lattice QCD with $N_f=2+1+1$ dynamical quark flavours
• Pion form factor and charge radius from Lattice QCD at physical point
• Flavor decomposition for the proton helicity parton distribution functions
• Flavor decomposition of the nucleon unpolarized, helicity and transversity parton distribution functions from lattice QCD simulations
• The role of zero-mode contributions in the matching for the twist-3 PDFs $e(x)$ and $h_L(x)$
• One-loop matching for the twist-3 parton distribution $g_T(x)$
• Parton physics from a heavy-quark operator product expansion: Formalism and Wilson coefficients
• Nucleon Gluon Distribution Function from 2+1+1-Flavor Lattice QCD
• Target Mass Effects in Parton Quasi-Distributions
• Positivity and renormalization of parton densities
• Reconstructing spectral functions via automatic differentiation
• Complementarity of experimental and lattice QCD data on pion parton distributions
• Parton distribution functions beyond leading twist from lattice QCD: The $h_L(x)$ case
• Strong coupling constant from moments of quarkonium correlators revisited
• Continuum limit of parton distribution functions from the pseudo-distribution approach on the lattice
• Towards studying the structural differences between the pion and its radial excitation
• Quark distribution inside a pion in many-flavor (2 + 1)-dimensional QCD using lattice computations: UV listens to IR
• Chiral Perturbation for Large Momentum Effective Field Theory
• Parton physics of the large-$N_c$ mesons

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