Article

# Moving Multi-Channel Systems in a Finite Volume

04/2012;
Source: arXiv

ABSTRACT The spectrum of a system with multiple channels composed of two hadrons with
nonzero total momentum is determined in a finite volume with periodic boundary
conditions using effective field theory methods. The results presented are
accurate up to exponentially suppressed corrections in the volume. The
formalism allows one to determine the phase shifts and mixing parameters of
$\pi\pi-KK$ isosinglet coupled channels directly from Lattice Quantum
Chromodynamics. We show that the extension to more than two channels is
straightforward and present the result for the three channels. From the energy
quantization condition, the volume dependence of electroweak matrix elements of
two-hadron processes is extracted, for both relativistic and non-relativistic
systems. In the NR case, we pay close attention to processes that mix the
$\singlet-\triplet$ two-nucleon states, e.g. proton-proton fusion
($pp\rightarrow d+e^++\nu_e$), and show how to determine the transition
amplitude of such processes directly from lattice QCD.

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### Keywords

$\pi\pi-KK$ isosinglet

$\singlet-\triplet$ two-nucleon states

effective field theory methods

electroweak matrix elements

exponentially suppressed corrections

finite volume

lattice QCD

nonzero total momentum

NR case

phase shifts

relativistic