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 gr
aphs must be summed, which leads to a cutoff dependence that does not appea
r 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 cor
responding scattering length is used as input. We also obtain a model-indep
endent 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. (C) 1999 Elsevier S
cience B.V.