K→ππ decays in a finite volume Original Research Article

We discuss finite-volume computations of two-body hadronic decays below the inelastic threshold (e.g., K→ππ decays). The relation between finite-volume matrix elements and physical amplitudes, recently derived by Lellouch and Lüscher, is extended to all elastic states under the inelastic threshold. We present a detailed comparison of our approach with that of Lellouch and Lüscher and discuss the possible limitations of the method which could arise due to the presence of inelastic thresholds. We also examine a standard alternative method which can be used to extract the real part of the decay amplitude from correlators of the form 〈0|T[ππHWK]|0〉. We show that in this case there are finite-volume corrections which vanish as inverse powers of the volume, which cannot be removed by a multiplicative factor.