The chiral logs of the K -> pi pi amplitude

I calculate the leading logarithmic contributions up to two-loop order of the octet part of the K -> pi pi amplitude. This sector of the weak chiral Lagrangian is believed to be the main source of the enhancement of the I=0 relative to the I=2 K -> pi pi amplitude, the so-called Delta I = 1/2 rule. I discuss the procedure of chiral extrapolations of lattice data specific to K -> pi pi decays and study the implication of the present calculation on these numerically. The latter reinforces the fact that one has to expect a large enhancement of the I=0 part of the amplitude due to re-scattering effects between the three mesons.