The chiral logs of the K->ππ amplitude

I calculate the leading logarithmic contributions up to two-loop order of the octet part of the K0->ππ 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=2K0->ππ amplitude, the so-called ΔI=1/2 rule. I discuss the procedure of chiral extrapolations of lattice data specific to K->ππdecays 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