The spectrum of a system with multiple channels composed of two hadrons with nonzero total momentum is determined in a finite cubic volume with periodic boundary conditions using effective field theory methods. The results presented are accurate up to exponentially suppressed corrections in the volume due to the finite range of hadronic interactions. 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 three channels. From the energy quantization condition, the volume dependence of electroweak matrix elements of two-hadron processes is extracted. In the nonrelativistic case, we pay close attention to processes that mix the ${}^{1}S_0-{}^{3}S_1$ two-nucleon states, e.g. proton-proton fusion ($pp\to d+e^{+}+{\nu }_e$), and show how to determine the transition amplitude of such processes directly from lattice QCD.

• Received 23 April 2012

DOI:https://doi.org/10.1103/PhysRevD.88.094507