Effective electroweak Hamiltonian in the gradient-flow formalism

The effective electroweak Hamiltonian in the gradient-flow formalism is constructed for the current-current operators through next-to-next-to-leading-order QCD. The results are presented for two common choices of the operator basis. This allows for a consistent matching of perturbatively evaluated Wilson coefficients and nonperturbative matrix elements evaluated by lattice simulations on the basis of the gradient-flow formalism.