The gradient-flow coupling in QED is just the Laplace transform of the regular photon polarization function. Among other things, this paper studies the renormalization group structure of three-dimensional QED in this scheme.

We provide the results for important observables in the gradient-flow formalism including effects from a massive quark.

Here we provide crucial input for the determination of parton density function on the lattice using the gradient flow formalism, see this paper.

This is a demonstration of how the gradient flow allows one to circumvent the fundamental obstacles that prohibit the determination of parton density functions (PDFs) from first principle lattice calculations. It evaluates the PDFs for the pion and shows that they agree with phenomenological extractions.

Using the small-flow-time expansion in the gradient-flow formalism, we use the PCAC relation to obtain the strange and charm quark mass by combining the perturbative results for the matching coefficients of the quark currents with lattice data.