Low-Energy Expansion for Elastic Three-Body Scattering

It is shown that the connected scattering amplitude for three free particles may be written (as the three-body energy $E$ goes to zero) in the form $A{E}^{-1\mathrm{}}+B{E}^{\frac{-1\mathrm{}}{2}}+C\ln E+O\left(1\right)\mathrm{}$ with $A$, $B$, and $C$ completely determined by kinematics and the two-body scattering amplitudes at zero energy.