Towards a non-perturbative calculation of Weak Hamiltonian Wilson coefficients

We propose a method to compute the Wilson coefficients of the weak effective Hamiltonian to all orders in the strong coupling constant using Lattice QCD simulations. We perform our calculations adopting an unphysically light weak boson mass of around $2\mathrm{G}\mathrm{e}\mathrm{V}$. We demonstrate that systematic errors for the Wilson coefficients $C_1$ and $C_2$, related to the current-current four-quark operators, can be controlled and present a path towards precise determinations in subsequent works.