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

Abstract

We present the ingredients necessary for the determination of physical K→ ππ decay amplitudes for Δ I=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 I=2〈ππ| O W|K〉 , where O W is one of the operators appearing in the Δ S=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.