QCD field-strength correlators on a Polyakov loop with gradient flow at next-to-leading order

Momentum exchange between a heavy quark and a hot quark-gluon medium can be characterized nonperturbatively in terms of field-strength field-strength (E-E and B-B) correlators along a Polyakov loop. These can be studied on the lattice and analytically continued. However the lattice typically determines the correlators after the application of gradient flow. We investigate how gradient flow renormalizes these correlation functions by carrying out a next-to-leading order perturbative analysis of the correlators including gradient flow. This establishes a next-to-leading order renormalization matching between the correlators as measured on the lattice and the correlators relevant for momentum diffusion.