  We discuss general one and two-loop banana diagrams and one-loop diagrams
with external lines with arbitrary masses on the anti de Sitter spacetime by
using methods of AdS quantum field theory in the dimensional regularization
approach. The banana diagrams explicitly computed in this paper are indeed the
necessary ingredients for the evaluation of the two-loop effective potential of
the Standard Model and can be used to extend the flat space results in in
presence of a negative cosmological constant. In the one-loop case we also
compute the effective potential for an $O(N)$ model in $d=4$ dimension as an
explicit function of the cosmological constant $\Lambda$, both exactly and
perturbatively up to order $\Lambda$. In the two-loop case we show the explicit
calculation is possible thanks to a remarkable discrete K\"all\'en-Lehmann
formula which we found and proved sometimes ago and whose domain of
applicability we extend in the present paper.
