Non-perturbative renormalization of the $\mathrm{\Delta }S=2$ operator and the heavy-light axial current

We apply a recently introduced non-perturbative renormalization method to two types of lattice operators: the $\mathrm{\Delta }S=2$ four fermion operator and the heavy-light static axial current, which are relevant for the physics of $K$ and $B$ mesons respectively. The results of the non-perturbative calculations of the renormalization constants are compared with the corresponding perturbative ones.