The gradient flow coupling from numerical stochastic perturbation theory

TL;DR

This paper explores the use of numerical stochastic perturbation theory to compute gradient flow observables more efficiently, addressing challenges in perturbative calculations and aiming for precise results with reduced computational costs.

Contribution

It introduces new algorithmic developments that significantly lower the computational cost of perturbative calculations of gradient flow observables.

Findings

Reduced computational cost for perturbative calculations

Improved control over statistical and systematic uncertainties

Successful matching of ${ar{\rm MS}}$ and gradient flow couplings

Abstract

Perturbative calculations of gradient flow observables are technically challenging. Current results are limited to a few quantities and, in general, to low perturbative orders. Numerical stochastic perturbation theory is a potentially powerful tool that may be applied in this context. Precise results using these techniques, however, require control over both statistical and systematic uncertainties. In this contribution, we discuss some recent algorithmic developments that lead to a substantial reduction of the cost of the computations. The matching of the ${\overline{\rm MS}}$ coupling with the gradient flow coupling in a finite box with Schr\"odinger functional boundary conditions is considered for illustration.