Hadronic vacuum polarization using gradient flow

TL;DR

This paper develops a new method using gradient flow to compute hadronic vacuum polarization functions in QCD, providing a more efficient approach for lattice evaluations and deriving flow-time evolution equations for relevant operators.

Contribution

It introduces the gradient-flow operator product expansion for QCD correlators up to NNLO and derives flow-time evolution equations for dimension-four operators.

Findings

Operator product expansion calculated through NNLO

Flow-time evolution equations derived for dimension-four operators

Provides an alternative, efficient lattice evaluation method

Abstract

The gradient-flow operator product expansion for QCD current correlators including operators up to mass dimension four is calculated through NNLO. This paves an alternative way for efficient lattice evaluations of hadronic vacuum polarization functions. In addition, flow-time evolution equations for flowed composite operators are derived. Their explicit form for the non-trivial dimension-four operators of QCD is given through order $\alpha_s^3$.