Finite Volume Effects in Weak Hadronic Decays

TL;DR

This paper discusses how finite-volume calculations of two-body hadronic decays can be related to physical decay amplitudes, extending existing methods to all elastic states below inelastic thresholds and deriving the quantization condition in quantum field theory.

Contribution

It extends the Lellouch-Lüscher relation to all elastic states below inelastic thresholds and provides a quantum field theory derivation of the Lüscher quantization condition.

Findings

Extended the Lellouch-Lüscher relation to all elastic states below inelastic thresholds

Derived the Lüscher quantization condition directly in quantum field theory

Clarified the connection between finite-volume matrix elements and physical decay amplitudes

Abstract

In this talk we discuss finite-volume computations of two-body hadronic decays below the inelastic threshold (e.g. $K\to\pi\pi$ decays). In particular we show how the relation between finite-volume matrix elements and physical amplitudes, recently derived by Lellouch and L\"uscher, can be extended to all elastic states under the inelastic threshold. We also provide a derivation of the L\"uscher quantization condition directly in quantum field theory.