Three-body system in leading order Effective Field Theory without three-body forces

Abstract

The use of leading order effective field theory (EFT) to describe neutron-deuteron scattering leads to integral equations that have unusual behaviour: when only two-body interactions are included, the scattering amplitude does not approach a limit when the cutoff used to solve the equations is removed. It has recently been shown that this cutoff dependence can be eliminated by the careful inclusion of a three-body force. In this paper we show that the cutoff dependence is just a reflection of the fact that the aforementioned integral equations admit an infinite number of solutions amongst which only one corresponds to the physical scattering amplitude. We show how to numerically extract the physical scattering amplitude from the general solution and in this way explicitly demonstrate that the amplitude for a particle scattering off a two-body bound state, in leading order EFT, is in fact determined entirely by two-body forces.