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

The inferred value of the relic density from cosmological observations has reached a precision that is akin to that of the LEP precision measurements. This level of precision calls for the evaluation of the annihilation cross sections of dark matter that goes beyond tree-level calculations as currently implemented in all codes for the computation of the relic density. In supersymmetry radiative corrections are known to be large and thus must be implemented. Full one-loop radiative corrections for many annihilation processes have been performed. It is important to investigate whether the bulk of these corrections can be parameterised through an improved Born approximation that can be implemented as a selection of form factors to a tree-level code. This paper is a second in a series that addresses this issue. After having provided these form factors for the annihilation of the neutralinos into fermions, which cover the case of a bino-like LSP (Lightest Supersymmetric Particle), we turn our attention here to a higgsino-like dark matter candidate through its annihilation into $ZZ$. We also investigate the cases of a mixed LSP. In all cases we compare the performance of the form factor approach with the result of a full one-loop correction. We also study the issue of the renormalisation scheme dependence. An illustration of the phenomenon of non decoupling of the heavy sfermions that takes place for the annihilation of the lightest neutralino into $ZZ$ is also presented.