Finite-volume Hamiltonian method for coupled channel interactions in lattice QCD

Within a multi-channel formulation of $\pi \pi$ scattering, we investigate the use of the finite-volume Hamiltonian approach to resolve scattering observables from lattice QCD spectra. The asymptotic matching of the well-known L"uscher formalism encodes a unique finite-volume spectrum. Nevertheless, in many practical situations, such as coupled-channel systems, it is advantageous to interpolate isolated lattice spectra in order to extract physical scattering parameters. Here we study the use of the Hamiltonian framework as a parameterisation that can be fit directly to lattice spectra. We find that with a modest amount of lattice data, the scattering parameters can be reproduced rather well, with only a minor degree of model dependence.