A novel nonperturbative renormalization scheme for local operators

TL;DR

This paper introduces a new nonperturbative renormalization scheme for local operators in lattice QCD using the gradient flow, enabling more accurate determination of operator running and matching to standard schemes.

Contribution

It proposes a novel renormalization scheme based on the gradient flow for local fermionic operators, suitable for nonperturbative lattice QCD computations.

Findings

Preliminary results show the scheme effectively determines the running of quark bilinear operators.

The method facilitates perturbative matching to the MS-bar scheme.

Gradient flow suppresses ultraviolet divergences in a controlled manner.

Abstract

The gradient flow exponentially suppresses ultraviolet field fluctuations and removes ultraviolet divergences (up to a multiplicative fermionic wavefunction renormalization). It can be used to describe real-space Wilsonian renormalization group transformations and determine the corresponding beta function. We propose a new nonperturbative renormalization scheme for local composite fermionic operators that uses the gradient flow and is amenable to lattice QCD calculations. We present preliminary nonperturbative results for the running of quark bilinear operators in this scheme and outline the calculation of perturbative matching to the MS-bar scheme.