Automatized full one-loop renormalization of the MSSM: The Higgs sector, the issue of tanβ and gauge invariance

We give an extensive description of the renormalization of the Higgs sector of the minimal super-symmetric model in SLOOPS. SLOOPS is an automatized code for the computation of one-loop processes in the MSSM. In this paper, the first in a series, we study in detail the nongauge invariance of some definitions of tan beta. We rely on a general nonlinear gauge-fixing constraint to make the gauge parameter dependence of different schemes for tan beta explicit at one loop. In so doing, we update, within these general gauges, an important Ward-Slavnov-Taylor identity on the mixing between the pseudoscalar Higgs, A(0), and Z(0). We then compare the tan beta scheme dependence of a few observables. We find that the best tan beta scheme is the one based on the decay A(0) -> tau(+)tau(-) because of its gauge invariance, because it is unambiguously defined from a physical observable, and because it is numerically stable. The oft used (DR) over bar scheme performs almost as well on the last count, but is usually defined from nongauge-invariant quantities in the Higgs sector. The use of the heavier scalar Higgs mass in lieu of tan beta, though related to a physical parameter, induces radiative corrections that are too large in many instances, and is therefore not recommended.