Unlocking higher-order moments of parton distribution functions from lattice QCD

TL;DR

This paper introduces a novel lattice QCD method utilizing gradient flow to compute higher-order moments of parton distribution functions, enabling multiplicative renormalization and improved computational efficiency.

Contribution

The authors develop a new approach using gradient flow for lattice QCD to calculate moments of any order, with simplified renormalization and matching procedures.

Findings

Derived one-loop matching coefficients for non-singlet moments.

Demonstrated multiplicative renormalization for twist-2 operators.

Enhanced signal-to-noise ratio in lattice computations.

Abstract

We present a new method to calculate moments of parton distribution functions of any order with lattice QCD computations. This method leverages the gradient flow for fermion and gauge fields. The flowed matrix elements of twist-2 operators renormalize multiplicatively, and the matching with physical matrix elements is achieved through the use of continuum symmetries. We derive the matching coefficients at one-loop in perturbation theory for moments of any order in the flavor non-singlet case and provide specific examples of operators suitable for lattice QCD computations. The multiplicative renormalization and matching are independent of the choice of Lorentz indices, allowing the use of temporal indices for twist-2 operators of any dimension. This approach should then also significantly enhance the signal-to-noise ratio in the computation of moments.