Benchmark calculations for elastic fermion-dimer scattering

TL;DR

This paper combines continuum and lattice methods to accurately calculate elastic scattering parameters between a fermion and a dimer, with implications for atomic and nuclear physics.

Contribution

It introduces a precise lattice calculation of fermion-dimer scattering using finite-volume methods and accounts for finite-volume corrections, validating results against continuum STM equation calculations.

Findings

Lattice and continuum results for scattering length agree within uncertainties.

Finite-volume corrections significantly improve lattice calculation accuracy.

Results applicable to cold atomic gases and nuclear scattering studies.

Abstract

We present continuum and lattice calculations for elastic scattering between a fermion and a bound dimer in the shallow binding limit. For the continuum calculation we use the Skorniakov-Ter-Martirosian (STM) integral equation to determine the scattering length and effective range parameter to high precision. 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 kappa a_fd = 1.174(9) and kappa r_fd = -0.029(13). These results agree well with the continuum values kappa a_fd = 1.17907(1) and kappa r_fd = -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.