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Multiple-channel generalization of Lellouch-Lüscher formula

Maxwell T. Hansen^* and Stephen R. Sharpe^†

Physics Department, University of Washington, Seattle, Washington 98195-1560, USA

^*mth28@uw.edu
^†srsharpe@uw.edu

Phys. Rev. D 86, 016007 – Published 19 July, 2012

DOI: https://doi.org/10.1103/PhysRevD.86.016007

Abstract

We generalize the Lellouch-Lüscher formula, relating weak matrix elements in finite and infinite volumes, to the case of multiple strongly coupled decay channels into two scalar particles. This is a necessary first step on the way to a lattice quantum chromodynamics calculation of weak decay rates for processes such as $D \to π π$ and $D \to K \bar{K}$ . We also present a field theoretic derivation of the generalization of Lüscher’s finite-volume quantization condition to multiple two-particle channels. We give fully explicit results for the case of two channels, including a form of the generalized Lellouch-Lüscher formula expressed in terms of derivatives of the energies of finite-volume states with respect to the box size. Our results hold for arbitrary total momentum and for degenerate or nondegenerate particles.

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Multiple-channel generalization of Lellouch-Lüscher formula

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