  In order to predict the cosmological abundance of dark matter, an estimation
of particle rates in an expanding thermal environment is needed. For thermal
dark matter, the non-relativistic regime sets the stage for the freeze-out of
the dark matter energy density. We compute transition widths and annihilation,
bound-state formation, and dissociation cross sections of dark matter fermion
pairs in the unifying framework of non-relativistic effective field theories at
finite temperature, with the thermal bath modeling the thermodynamical
behaviour of the early universe. We reproduce and extend some known results for
the paradigmatic case of a dark fermion species coupled to dark gauge bosons.
The effective field theory framework allows to highlight their range of
validity and consistency, and to identify some possible improvements.
