Universal formula for the flavor non-singlet axial-vector current from the gradient flow

TL;DR

This paper derives a universal, regularization-independent formula for the flavor non-singlet axial-vector current using the gradient flow, ensuring correct normalization and compatibility with the triangle anomaly across different regularizations.

Contribution

The authors present a novel universal formula for the axial-vector current derived via the gradient flow, applicable to lattice and continuum regularizations.

Findings

Formula holds independently of regularization.

Confirmed compatibility with the triangle anomaly.

Applicable to lattice regularization.

Abstract

By employing the gradient/Wilson flow, we derive a universal formula that expresses a correctly normalized flavor non-singlet axial-vector current of quarks. The formula is universal in the sense that it holds independently of regularization and especially holds with lattice regularization. It is also confirmed that, in the lowest non-trivial order of perturbation theory, the triangle diagram containing the formula and two flavor non-singlet vector currents possesses non-local structure that is compatible with the triangle anomaly.