Finite volume renormalization scheme for fermionic operators

TL;DR

This paper introduces a novel finite volume renormalization scheme utilizing Gradient Flow for fermionic and gauge fields, enabling nonperturbative scale dependence analysis through step-scaling, with initial results for pseudo-scalar density.

Contribution

It presents a new nonperturbative renormalization scheme based on Gradient Flow applicable to fermionic operators in finite volume.

Findings

Preliminary results for pseudo-scalar density in quenched approximation

Scheme allows nonperturbative scale dependence determination

Uses step-scaling similar to Schrödinger functional method

Abstract

We propose a new finite volume renormalization scheme. Our scheme is based on the Gradient Flow applied to both fermion and gauge fields and, much like the Schr\"odinger functional method, allows for a nonperturbative determination of the scale dependence of operators using a step-scaling approach. We give some preliminary results for the pseudo-scalar density in the quenched approximation.