Multiple-channel generalization of Lellouch-Luscher formula

Details Multiple-channel generalization of Lellouch-Luscher formula Multiple-channel generalization of Lellouch-Luscher formula

2012-04-03

arxiv.org/abs/1204.0826v3

Physics

High Energy Physics

High Energy Physics - Lattice

16 pages, 2 figures. Added references, clarified relation to and corrected comments about previous work, and minor stylistic i

Scientific paper

We generalize the Lellouch-Luscher 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 QCD calculation of weak decay rates for processes such as D -> pi pi and D -> KK. We also present a field theoretic derivation of the generalization of Luscher'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-Luscher 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 non-degenerate particles.

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