Valence Quark PDFs of the Proton from Two-Current Correlations in Lattice QCD

Abstract

Following previous works on that topic, we consider Euclidean hadronic matrix elements in position space of two spatially separated local currents on the lattice, in order to extract the $x$ dependence of parton distribution functions (PDFs). The corresponding approach is often referred to by the term lattice cross section. In this work we will consider valence quark PDFs of an unpolarized proton. We adapt the previously established formalism to our choice of operators. The calculation of the two-current matrix elements requires the evaluation of four-point functions. The corresponding calculation is carried out on a $n_f=2+1$ gauge ensemble with lattice spacing $a=0.0856\mathrm{fm}$ and pseudoscalar masses $m_{\pi }=355\mathrm{MeV}$ and $m_K=441\mathrm{MeV}$. The four-point functions have been evaluated in a previous project. The lattice data is converted to the $\overline{\mathrm{MS}}$ scheme at a scale $\mu =2\mathrm{GeV}$ and improved with respect to lattice artifacts. We use a common model as fit ansatz for the lattice data in order to extract the PDFs.

arXiv comment11 pages, 6 figures

References in corpus (33)

• Parton Physics on Euclidean Lattice
• Simulation of QCD with N_f=2+1 flavors of non-perturbatively improved Wilson fermions
• Constraints on large-$x$ parton distributions from new weak boson production and deep-inelastic scattering data
• Parton distributions and lattice QCD calculations: a community white paper
• Large-Momentum Effective Theory
• Exploring hadrons' partonic structure using ab initio lattice QCD calculations
• 50 Years of Quantum Chromodynamics
• 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
• Elements of a theory for multiparton interactions in QCD
• Deep-inelastic scattering and the operator product expansion in lattice QCD
• Pion Valence Quark Distribution from Matrix Element Calculated in Lattice QCD
• Nonperturbative Evolution of Parton Quasi-Distributions
• Pion distribution amplitude from Euclidean correlation functions: Exploring universality and higher-twist effects
• Approximate N${}^3$LO Parton Distribution Functions with Theoretical Uncertainties: MSHT20aN${}^3$LO PDFs
• Reconstructing parton distribution functions from Ioffe time data: from Bayesian methods to Neural Networks
• Pion valence quark distribution from current-current correlation in lattice QCD
• The x-dependence of hadronic parton distributions: A review on the progress of lattice QCD
• Confronting lattice parton distributions with global QCD analysis
• Flavor decomposition of the nucleon unpolarized, helicity and transversity parton distribution functions from lattice QCD simulations
• Unpolarized proton PDF at NNLO from lattice QCD with physical quark masses
• Octet baryon isovector charges from $N_f=2+1$ lattice QCD
• Complementarity of experimental and lattice QCD data on pion parton distributions
• Continuum limit of parton distribution functions from the pseudo-distribution approach on the lattice
• Nonperturbative Renormalization in Lattice QCD with three Flavors of Clover Fermions: Using Periodic and Open Boundary Conditions
• Overview of lattice calculations of the $x$-dependence of PDFs, GPDs and TMDs
• Non-singlet quark helicity PDFs of the nucleon from pseudo-distributions
• Lattice results for the longitudinal spin structure and color forces on quarks in a nucleon
• Double parton distributions in the pion from lattice QCD
• Double parton distributions in the nucleon from lattice QCD
• Double parton distributions with flavor interference from lattice QCD