We analyze the validity of the theorems concerning the cancellation of the infrared and collinar divergences in the case of dark matter freeze-out in the early universe.
In particular,
we compute the electroweak logarithmic corrections of infrared origin to the annihilation cross section of a dark matter particle being the neutral component of a
SU(2)$_L$ multiplet.
The inclusion of processes with final state $W$ can modify significantly the
cross sections computed with only virtual $W$ exchange.
Our results show that the inclusion of infrared logs is necessary for a precise
computation of the dark matter relic abundance.
