Abstract:
We study the three-body system with short-range interactions
characterized by an unnaturally large two-body scattering
length. We show that the off-shell scattering amplitude is
cutoff independent up to power corrections. This allows us
to derive an exact renormalization group equation for the
three-body force. We also obtain a renormalized equation for
the off-shell scattering amplitude. This equation is
invariant under discrete scale transformations. The
periodicity of the spectrum of bound states originally
observed by Efimov is a consequence of this symmetry. The
functional dependence of the three-body scattering length on
the two-body scattering length can be obtained analytically
using the asymptotic solution to the integral equation. An
analogous formula for the three-body recombination
coefficient is also obtained.