Moments of parton distribution functions of any order from lattice QCD

Abstract

We describe a procedure to determine moments of parton distribution functions of any order in lattice quantum chromodynamics (QCD). The procedure is based on the gradient flow for fermion and gauge fields. The flowed matrix elements of twist-2 operators renormalize multiplicatively, and the matching with the physical matrix elements can be obtained using continuum symmetries and the irreducible representations of Euclidean 4-dimensional rotations. We calculate the matching coefficients at one-loop in perturbation theory for moments of any order in the flavor nonsinglet case. We also give specific examples of operators that could be used in lattice QCD computations. It turns out that it is possible to choose operators with identical Lorentz indices and still have a multiplicative matching. One can thus use twist-2 operators exclusively with temporal indices, thus substantially improving the signal-to-noise ratio in the computation of the hadronic matrix elements.

arXiv comment10 pages, 2 figures - Version matches published version

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• Parton Distribution Functions in the Schwinger model from Tensor Network States
• Mapping Parton Distributions of Hadrons with Lattice QCD
• Generalized Parton Distributions from Lattice QCD with Asymmetric Momentum Transfer: Unpolarized Quarks at Nonzero Skewness
• Large-Momentum Effective Theory's Asymptotic Extrapolation vs the Inverse Problem
• Two-loop gradient-flow renormalization of scalar QCD
• A Unified Neural-Network Framework for Nucleon Imaging from Numerical Simulations of QCD
• Accessing the Gluon Momentum Fraction of Nucleons through the Gradient Flow