Two-loop Higgs mass calculation from a diagrammatic approach

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.