K→ππ decays in SU(2) Chiral Perturbation Theory

We study the decays K→ππ in one-loop two-flavour Chiral Perturbation Theory. We provide arguments why the calculation of the coefficient of the pionic chiral logarithm ℓM=M2logM2 is unique and then perform the calculation. As a check we perform the reduction of the known three-flavour result. Our result can be used to perform the extrapolation to the physical pion mass of direct lattice QCD calculations of K→ππ at fixed ms or mK2. The underlying arguments are expected to be valid for heavier particles and other processes as well.