$K^{+}\toπ^{+}π^{0}$ decays at next-to-leading order in the chiral expansion on finite volumes

Abstract

We present the ingredients for determining $K^{+}\toπ^{+}π^{0}$ matrix elements via the combination of lattice QCD and chiral perturbation theory ($χ$PT). By simulating these matrix elements at unphysical kinematics, it is possible to determine all the low-energy constants (LECs) for constructing the physical $K^{+}\toπ^{+}π^{0}$ amplitudes at next-to-leading order (NLO) in the chiral expansion. In this work, the one-loop chiral corrections are calculated for arbitrary meson four-momenta, in both $χ$PT and quenched $χ$PT (q$χ$PT), and the finite-volume effects are studied.