The gradient flow at higher orders in perturbation theory

TL;DR

This paper reviews advanced higher-order perturbative calculations within the gradient-flow formalism, focusing on the beta function, small-flow-time expansions, and systematic integral expansions using the strategy of regions.

Contribution

It provides a comprehensive review of higher-order results and introduces systematic expansion techniques for gradient-flow integrals at different flow times.

Findings

Calculated the gradient-flow beta function at higher orders

Derived small-flow-time expansions for key observables

Outlined the strategy of regions for systematic integral expansions

Abstract

Various results for higher-order perturbative calculations in the gradient-flow formalism are reviewed, including the gradient-flow beta function and the small-flow-time expansion of the hadronic vacuum polarization and the energy-momentum tensor. In addition, the strategy of regions is outlined in order to obtain systematic expansions of gradient-flow integrals, for example at large and small flow times.