K⁺ -> π⁺ π⁰ decays on finite volumes and at next-to-leading order in the chiral expansion

We present the ingredients necessary for the determination of physical K->ππ decay amplitudes for ΔI = 3/2 transitions, from lattice simulations at unphysical kinematics and the use of chiral perturbation theory at next-to-leading order. In particular we derive the expressions for the matrix elements <ππI=2|OW|K>, where OW is one of the operators appearing in the ΔS=1 weak Hamiltonian, in terms of low-energy constants at next-to-leading order in the chiral expansion. The one-loop chiral corrections are evaluated for arbitrary masses and momenta, both in full QCD and in the quenched approximation. We also investigate the finite-volume effects in this procedure