K→ππ amplitudes from Lattice QCD with a light charm quark

We compute the leading-order low-energy constants of the ΔS=1 effective weak Hamiltonian in the quenched approximation of QCD with up, down, strange, and charm quarks degenerate and light. They are extracted by comparing the predictions of finite-volume chiral perturbation theory with lattice QCD computations of suitable correlation functions carried out with quark masses ranging from a few MeV up to half of the physical strange mass. We observe a ΔI=1/2 enhancement in this corner of the parameter space of the theory. Although matching with the experimental result is not observed for the ΔI=1/2 amplitude, our computation suggests large QCD contributions to the physical ΔI=1/2 rule in the GIM limit, and represents the first step to quantify the role of the charm-quark mass in K→ππ amplitudes. The use of fermions with an exact chiral symmetry is an essential ingredient in our computation.