  We apply a field-theoretic functional renormalization group technique to the
few-body (vacuum) physics of non-relativistic atoms near a Feshbach resonance.
Three systems are considered: one-component bosons with U(1) symmetry,
two-component fermions with U(1)\times SU(2) symmetry and three-component
fermions with U(1) \times SU(3) symmetry. We focus on the scale invariant
unitarity limit for infinite scattering length. The exact solution for the
two-body sector is consistent with the unitary fixed point behavior for all
considered systems. Nevertheless, the numerical three-body solution in the
s-wave sector develops a limit cycle scaling in case of U(1) bosons and SU(3)
fermions. The Efimov parameter for the one-component bosons and the
three-component fermions is found to be approximately s=1.006, consistent with
the result of Efimov.
