  In the systems of spin $\frac12$ fermions with resonant $S$-wave interactions
supporting only weakly bound dimers the antisymmetry forbids recombination of
three (or more) fermions at zero energy. However, the fermion-fermion-dimer
recombination is only partially suppressed. It is studied in the framework of
momentum-space integral equations for the four-particle transition operators.
In the vicinity of the unitary limit the fermion-fermion-dimer recombination
rate, rescaled to build dimensionless quantity, is found to be linear in the
effective range parameter, enabling a simple and accurate parametrization as
well as evaluation of finite-range effects for any potential model. This
feature makes the present results very useful in benchmarking different methods
for three-cluster breakup and recombination calculations in four-particle
systems. The interplay of the three-fermion and fermion-fermion-dimer
recombination processes and their consequences for ultracold mixtures of
fermions and dimers is discussed.
