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We give an extensive description of the renormalisation of the Higgs sectorof the minimal supersymmetric model in SloopS. SloopS is an automatised codefor the computation of one-loop processes in the MSSM. In this paper, the firstin a series, we study in detail the non gauge invariance of some definitions oftan(beta). We rely on a general non-linear gauge fixing constraint to make thegauge parameter dependence of different schemes for tan(beta) at one-loopexplicit. In so doing, we update, within these general gauges, an importantWard-Slavnov-Taylor identity on the mixing between the pseudo-scalar Higgs,A^0, and the Z^0. We then compare the tan(beta) scheme dependence of a fewobservables. We find that the best tan(beta) scheme is the one based on thedecay A^0 -> tau^+ tau^- because of its gauge invariance, being unambiguouslydefined from a physical observable, and because it is numerically stable. Theoft used DRbar scheme performs almost as well on the last count, but is usuallydefined from non-gauge invariant quantities in the Higgs sector. The use of theheavier scalar Higgs mass in lieu of tan(beta) though related to a physicalparameter induces too large radiative corrections in many instances and istherefore not recommended.

Automatised full one-loop renormalisation of the MSSM I: The Higgs sector, the issue of tan(beta) and gauge invariance