The extracted value of the relic density has reached the few per-cent level precision. One can therefore no longer content oneself with calculations of this observable where the annihilation processes are computed at tree-level, especially in supersymmetry where radiative corrections are usually large. Implementing full one-loop corrections to all annihilation processes that would be needed in a scan over parameters is a daunting task. On the other hand one may ask whether the bulk of the corrections are taken into account through effective couplings of the neutralino that improve the tree-level calculation and would be easy to implement. We address this issue by concentrating in this first study on the neutralino coupling to i) fermions and sfermions and ii) Z. After constructing the effective couplings we compare their efficiency compared to the full one-loop calculation and comment on the failures and success of the approach. As a bonus we point out that large non decoupling effects of heavy sfermions could in principle be measured in the annihilation process, a point of interest in view of the latest limit on the squark masses from the LHC. We also comment on the scheme dependencies of the one-loop corrected results.
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