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.

14 pages, 16 figures

References in corpus (8)

• Simulation of QCD with N_f=2+1 flavors of non-perturbatively improved Wilson fermions
• Exploring hadrons' partonic structure using ab initio lattice QCD calculations
• A complete non-perturbative renormalization prescription for quasi-PDFs
• On the Renormalizability of Quasi Parton Distribution Functions
• Parton Distribution Function with Non-perturbative Renormalization from Lattice QCD
• 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

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