  We calculate the corrections to the Higgs mass in general theories restricted
to the case of massless gauge bosons (the gaugeless limit). We present analytic
expressions for the two-loop tadpole diagrams, and corresponding expressions
for the zero-momentum limit of the Higgs self energies, equivalent to the
second derivative of the two-loop effective potential. We describe the
implementation in SARAH, which allows an efficient, accurate and rapid
evaluation for generic theories. In the appendix, we provide the expressions
for tadpole diagrams in the case of massive gauge bosons.
