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The inferred value of the relic density from cosmological observations hasreached a precision that is akin to that of the LEP precision measurements.This level of precision calls for the evaluation of the annihilation crosssections of dark matter that goes beyond tree-level calculations as currentlyimplemented in all codes for the computation of the relic density. Insupersymmetry radiative corrections are known to be large and thus must beimplemented. Full one-loop radiative corrections for many annihilationprocesses have been performed. It is important to investigate whether the bulkof these corrections can be parameterised through an improved Bornapproximation that can be implemented as a selection of form factors to atree-level code. This paper is a second in a series that addresses this issue.After having provided these form factors for the annihilation of theneutralinos into fermions, which cover the case of a bino-like LSP (LightestSupersymmetric Particle), we turn our attention here to a higgsino-like darkmatter candidate through its annihilation into $ZZ$. We also investigate thecases of a mixed LSP. In all cases we compare the performance of the formfactor approach with the result of a full one-loop correction. We also studythe issue of the renormalisation scheme dependence. An illustration of thephenomenon of non decoupling of the heavy sfermions that takes place for theannihilation of the lightest neutralino into $ZZ$ is also presented.

Relic density calculations beyond tree-level, exact calculations versus effective couplings: the ZZ final state