  We discuss renormalization of the non-relativistic three-body problem with
short-range forces. The problem is non-perturbative at momenta of the order of
the inverse of the two-body scattering length. An infinite number of graphs
must be summed, which leads to a cutoff dependence that does not appear in any
order in perturbation theory. We argue that this cutoff dependence can be
absorbed in one local three-body force counterterm and compute the running of
the three-body force with the cutoff. This allows a calculation of the
scattering of a particle and the two-particle bound state if the corresponding
scattering length is used as input. We also obtain a model-independent relation
between binding energy of a shallow three-body bound state and this scattering
length. We comment on the power counting that organizes higher-order
corrections and on relevance of this result for the effective field theory
program in nuclear and molecular physics.
