  Heavy Majorana neutrinos enter in many scenarios of physics beyond the
Standard Model: in the original seesaw mechanism they provide a natural
explanation for the small masses of the Standard Model neutrinos and in the
simplest leptogenesis framework they are at the origin of the baryonic matter
of the universe. In this paper, we develop an effective field theory for
non-relativistic Majorana particles, which is analogous to the heavy-quark
effective theory. Then, we apply it to the case of a heavy Majorana neutrino
decaying in a hot and dense plasma of Standard Model particles, whose
temperature is much smaller than the mass of the Majorana neutrino but still
much larger than the electroweak scale. The neutrino width gets
zero-temperature contributions that can be computed from in-vacuum matrix
elements, and thermal corrections. Only the latter will be addressed. Symmetry
and power counting arguments made manifest by the effective field theory
restrict the form of the thermal corrections and simplify their calculation.
The final result agrees with recent determinations obtained with different
methods. The effective field theory presented here is suitable to be used for a
variety of different models involving non-relativistic Majorana fermions.
