The leading two loop divergences of the non-leptonic weak chiral Lagrangian

We calculate the leading divergences at NNLO for the octet part of the non-leptonic weak sector of chiral perturbation theory, using renormalization group methods. The role of counterterms which vanish at the equation of motion and their use to simplify the calculation is shown explicitly. The obtained counterterm Lagrangian can be employed to calculate the chiral double log contributions of quantities in this sector, most notably the K -> pi pi amplitude. The double log contribution of the latter is discussed in a separate paper.