Benchmark calculations for elastic fermion-dimer scattering

Abstract

We present continuum and lattice calculations for elastic scattering between a fermion and a bound dimer in the shallow binding limit. For the lattice calculation we use the finite-volume method of L\"uscher. We take into account topological finite-volume corrections to the dimer binding energy which depend on the momentum of the dimer. After subtracting these effects, we find from the lattice calculation $\ensuremath{\kappa}{a}_{fd}=1.174(9)$ and $\ensuremath{\kappa}{r}_{fd}=\ensuremath{-}0.029(13)$. These results agree well with the continuum values $\ensuremath{\kappa}{a}_{fd}=1.17907(1)$ and $\ensuremath{\kappa}{r}_{fd}=\ensuremath{-}0.0383(3)$ obtained from the STM equation. We discuss applications to cold atomic Fermi gases, deuteron-neutron scattering in the spin-quartet channel, and lattice calculations of scattering for nuclei and hadronic molecules at finite volume.