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Title: Multi-channel 1-to-2 transition amplitudes in a finite volume

We derive a model-independent expression for finite-volume matrix elements. Specifically, we present a relativistic, non-perturbative analysis of the matrix element of an external current between a one-scalar in-state and a two-scalar out-state. Our result, which is valid for energies below higher-particle inelastic thresholds, generalizes the Lellouch-Luscher formula in two ways: we allow the external current to inject arbitrary momentum into the system and we allow for the final state to be composed an arbitrary number of strongly coupled two-particle states with arbitrary partial waves (including partial-wave mixing induced by the volume). We also illustrate how our general result can be applied to some key examples, such as heavy meson decays and meson photo production. Finally, we point out complications that arise involving unstable resonance states, such as B to K*+l+l when staggered or mixed-action/partially-quenched calculations are performed.
 [1] ;  [2] ;  [3]
  1. JLAB
  2. Helmholtz Institute Mainz
  3. W&M. JLAB
Publication Date:
OSTI Identifier:
Report Number(s):
JLAB-THY-15-2006; DOE/OR/23177-3293; arXiv:1502.00540; NT@WM-15-03
FG02- 96ER40956
DOE Contract Number:
AC05-06OR23177; SC0012180
Resource Type:
Resource Relation:
Journal Name: PoS LATTICE2014; Conference: Lattice 2014, 23-28 Jun 2014. Brookhaven, NY, USA
Research Org:
Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
Sponsoring Org:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
Country of Publication:
United States