RI/MOM renormalization of the quasi-PDF in lattice regularization

Abstract

We analyze the lattice spacing dependence for the pion unpolarized matrix element of a quark bilinear operator with Wilson link (quasi-PDF operator) in the rest frame, using 13 lattice spacings ranging from 0.032 fm to 0.121 fm. We compare results for three different fermion actions with or without good chiral symmetry on dynamical gauge ensembles from three collaborations. This investigation is motivated by the fact that the gauge link generates an $1/a$ divergence, the cancelation of which in many ratios can be numerically tricky. Indeed, our results show that this cancelation deteriorates with decreasing lattice spacing, and that the RI/MOM method leaves a linearly divergent residue for quasi-PDFs. We also show that in the Landau gauge the interaction between the Wilson link and the external state results in a linear divergence which depends on the discretized fermion action.

arXiv comment14 pages, 16 figures

References in corpus (32)

• Exactly massless quarks on the lattice
• The Chroma Software System for Lattice QCD
• Parton Physics on Euclidean Lattice
• A construction of lattice chiral gauge theories
• A General Method for Non-Perturbative Renormalization of Lattice Operators
• Flavor Symmetry and the Static Potential with Hypercubic Blocking
• Solving Lattice QCD systems of equations using mixed precision solvers on GPUs
• Domain wall QCD with physical quark masses
• Simulation of QCD with N_f=2+1 flavors of non-perturbatively improved Wilson fermions
• Lattice QCD ensembles with four flavors of highly improved staggered quarks
• Exploring hadrons' partonic structure using ab initio lattice QCD calculations
• Extracting Parton Distribution Functions from Lattice QCD Calculations
• Factorization Theorem Relating Euclidean and Light-Cone Parton Distributions
• 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
• Reconstruction of light-cone parton distribution functions from lattice QCD simulations at the physical point
• 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
• Three loop anomalous dimension of non-singlet quark currents in the RI' scheme
• Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD
• Matching the Quasi Parton Distribution in a Momentum Subtraction Scheme
• Proton Isovector Helicity Distribution on the Lattice at Physical Pion Mass
• On the renormalization of quasi parton distribution
• Unpolarized isovector quark distribution function from Lattice QCD: A systematic analysis of renormalization and matching
• Self-Renormalization of Quasi-Light-Front Correlators on the Lattice
• Distribution Amplitudes of $K^{\ast }$ and $\varphi$ at Physical Pion Mass from Lattice QCD
• Lattice continuum-limit study of nucleon quasi-PDFs
• Multi-mass solvers for lattice QCD on GPUs
• GW fermion propagators and chiral condensate
• Heavy and Light Quarks with Lattice Chiral Fermions

Cited by in corpus (15)

• Pion and Kaon Distribution Amplitudes from Lattice QCD
• Nucleon Helicity Generalized Parton Distribution at Physical Pion Mass from Lattice QCD
• Transversity GPDs of the proton from lattice QCD
• Precision Control in Lattice Calculation of $x$-dependent Pion Distribution Amplitude
• Renormalization of transverse-momentum-dependent parton distribution on the lattice
• Towards the determination of the gluon helicity distribution in the nucleon from lattice quantum chromodynamics
• First Glimpse into the Kaon Gluon Parton Distribution Using Lattice QCD
• Pion Valence-Quark Generalized Parton Distribution at Physical Pion Mass
• Gluon Parton Distribution of the Nucleon from 2+1+1-Flavor Lattice QCD in the Physical-Continuum Limit
• Overview of lattice calculations of the $x$-dependence of PDFs, GPDs and TMDs
• One-Loop Hybrid Renormalization Matching Kernels for Quasi-Parton Distributions
• Non-singlet quark helicity PDFs of the nucleon from pseudo-distributions
• Nonperturbative renormalization of asymmetric staple-shaped operators in twisted mass lattice QCD
• Large-Momentum Effective Theory's Asymptotic Extrapolation vs the Inverse Problem
• Unpolarized gluon distribution in the nucleon from lattice quantum chromodynamics