  The radiatively-induced mass splitting between components of an electroweak
multiplet is typically of order 100 MeV. This is sufficient to endow the
charged components with macroscopically-observable lifetimes, and ensure an
electrically-neutral dark matter particle. We show that a commonly used
iterative procedure to compute radiatively-corrected pole masses can lead to
very different mass splittings than a non-iterative calculation at the same
loop order. By estimating the uncertainties of the two one-loop results, we
show that the iterative procedure is significantly more sensitive to the choice
of renormalisation scale and gauge parameter than the non-iterative method.
This can cause the lifetime of the charged component to vary by up to 12 orders
of magnitude if iteration is employed. We show that individual pole masses
exhibit similar scale-dependence regardless of the procedure, but that the
leading scale-dependent terms cancel when computing the mass splitting if and
only if the non-iterative procedure is employed. We show that this behaviour
persists at two-loop order: the precision of the mass splitting improves in the
non-iterative approach, but our results suggest that higher-order corrections
do not reduce the uncertainty in the iterative calculation enough to resolve
the problem at two-loop order. We conclude that the iterative procedure should
not be used for computing pole masses in situations where electroweak mass
splittings are phenomenologically relevant.
