Pion Valence Quark Distribution at Physical Pion mass of $N_f=2+1+1$ Lattice QCD

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.

arXiv comment11 pages, 9 figures, 2 tables

References in corpus (63)

• Parton distributions for the LHC
• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• The Chroma Software System for Lattice QCD
• Parton Physics on Euclidean Lattice
• A General Method for Non-Perturbative Renormalization of Lattice Operators
• Quasi-PDFs, momentum distributions and pseudo-PDFs
• Lattice QCD ensembles with four flavors of highly improved staggered quarks
• Parton distributions and lattice QCD calculations: a community white paper
• Large-Momentum Effective Theory
• Exploring hadrons' partonic structure using ab initio lattice QCD calculations
• Nucleon Helicity and Transversity Parton Distributions from Lattice QCD
• Flavor Structure of the Nucleon Sea from Lattice QCD
• Exclusive processes in position space and the pion distribution amplitude
• A Lattice Calculation of Parton Distributions
• Scaling studies of QCD with the dynamical HISQ action
• Factorization Theorem Relating Euclidean and Light-Cone Parton Distributions
• A complete non-perturbative renormalization prescription for quasi-PDFs
• Determination of the bottom quark mass from the ${\rm Y}(1S)$ system
• Perturbative Renormalization of quasi-PDFs
• 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
• Parton Distribution Function with Non-perturbative Renormalization from Lattice QCD
• Pion Valence Structure from Ioffe Time Pseudo-Distributions
• Transversity parton distribution functions from lattice QCD
• Updated Lattice Results for Parton Distributions
• First direct lattice-QCD calculation of the $x$-dependence of the pion parton distribution function
• Parton Distributions in Nucleons and Nuclei
• Valence parton distribution function of pion from fine lattice
• Unpolarized and helicity generalized parton distributions of the proton within lattice QCD
• Matching the Quasi Parton Distribution in a Momentum Subtraction Scheme
• Parton Distribution Functions of the Charged Pion Within The xFitter Framework
• Snowmass 2021 whitepaper: Proton structure at the precision frontier
• Proton Isovector Helicity Distribution on the Lattice at Physical Pion Mass
• Power corrections and renormalons in parton quasi-distributions
• 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
• Pion generalized parton distribution from lattice QCD
• Gluon Quasi-PDF From Lattice QCD
• Improved Parton Distribution Functions at Physical Pion Mass
• Unpolarized isovector quark distribution function from Lattice QCD: A systematic analysis of renormalization and matching
• Valence-Quark Distribution of the Kaon and Pion from Lattice QCD
• Nucleon Tomography and Generalized Parton Distribution at Physical Pion Mass from Lattice QCD
• Precision Studies of QCD in the Low Energy Domain of the EIC
• Pion and Kaon Distribution Amplitudes in the Continuum Limit
• Perturbative expansion of the energy of static sources at large orders in four-dimensional SU(3) gauge theory
• Self-Renormalization of Quasi-Light-Front Correlators on the Lattice
• Gradient flow and scale setting on MILC HISQ ensembles
• 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
• Continuum-extrapolated NNLO Valence PDF of Pion at the Physical Point
• Nucleon Helicity Generalized Parton Distribution at Physical Pion Mass from Lattice QCD
• Lattice continuum-limit study of nucleon quasi-PDFs
• Next-to-next-to-leading order corrections to quark Quasi parton distribution functions
• Origin and Resummation of Threshold Logarithms in the Lattice QCD Calculations of PDFs
• Resumming Quark's Longitudinal Momentum Logarithms in LaMET Expansion of Lattice PDFs
• Leading Power Accuracy in Lattice Calculations of Parton Distributions
• Renormalization of parton quasi-distributions beyond the leading order: spacelike vs. timelike
• Unpolarized proton PDF at NNLO from lattice QCD with physical quark masses
• Parton distribution functions on the lattice and in the continuum
• Pion Valence-Quark Generalized Parton Distribution at Physical Pion Mass
• One-Loop Hybrid Renormalization Matching Kernels for Quasi-Parton Distributions

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• Nucleon Helicity Parton Distribution Function in the Continuum Limit with Self-Renormalization
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• Probing heavy meson lightcone distribution amplitudes with heavy quark spin symmetry
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• Large-Momentum Effective Theory's Asymptotic Extrapolation vs the Inverse Problem
• Parton distribution and fragmentation functions with massive gluons
• Generalized Parton Distributions from Lattice QCD with Asymmetric Momentum Transfer: Unpolarized Quarks at Nonzero Skewness
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