Multiple-Channel Generalization of Lellouch-Lüscher Formula

Conference · Thu Nov 01 00:00:00 EDT 2012 · PoS

DOI:https://doi.org/10.22323/1.164.0127· OSTI ID:1542975

Hansen, Maxwell T. ^[1]; Sharpe, Stephen R. ^[2]

---

1. Fermilab
2. Washington U., Seattle

We describe a generalization of the Lellouch-L\'uscher formula to the case of multiple strongly-coupled decay channels. As in the original formula, our final result is a relation between weak matrix elements in finite and infinite volumes. Our extension is limited to final states with two scalar particles, with center of mass energies below the lowest three- or four-particle threshold. Otherwise the extension is general, accommodating any number of channels, arbitrary strong coupling between channels, as well as any form of weak decay operators in the matrix elements. Among many possible applications, we emphasize that this is a necessary first step on the way to a lattice-QCD calculation of weak decay rates for D -> pi pi and D -> K K-bar. Our results allow for arbitrary total momentum and hold for degenerate or non-degenerate particles.

• Research Organization: Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP)
• DOE Contract Number: AC02-07CH11359
• OSTI ID: 1542975
• Report Number(s): arXiv:1211.0511; FERMILAB-CONF-12-857-T; 1198026
• Journal Information: PoS, Vol. LATTICE2012; Conference: 30th International Symposium on Lattice Field Theory, Cairns, Australia, 06/24-06/29/2012
• Country of Publication: United States
• Language: English