  Low-energy effective field theory describing a nonrelativistic three-body
system is analyzed in the Wilsonian renormalization group (RG) method. No
effective auxiliary field (dimeron) that corresponds to two-body propagation is
introduced.
  The Efimov effect is expected in the case of an infinite two-body scattering
length, and is believed to be related to the limit cycle behavior in the
three-body renormalization group equations (RGEs). If the one-loop property of
the RGEs for the nonrelativistic system without the dimeron field, which is
essential in deriving RGEs in the two-body sector, persists in the three-body
sector, it appears to prevent the emergence of limit cycle behavior. We explain
how the multi-loop diagrams contribute in the three-body sector without
contradicting the one-loop property of the RGEs, and derive the correct RGEs,
which lead to the limit cycle behavior. The Efimov parameter, $s_{0}$, is
obtained within a few percent error in the leading orders. We also remark on
the correct use of the dimeron formulation.
  We find rich RG-flow structure in the three-body sector. In particular, a
novel nontrivial fixed point of the three-body couplings is found when the
two-body interactions are absent. We also find, on the two-body nontrivial
fixed point, the limit cycle is realized as a loop of finite size in the space
of three-body coupling constants when terms with derivatives are included.
