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 supersymmetric 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 tanβ. We rely on a general nonlinear gauge-fixing constraint to make the gauge parameter dependence of different schemes for tanβ 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, A0, and Z0. We then compare the tanβ scheme dependence of a few observables. We find that the best tanβ scheme is the one based on the decay A0→τ+τ- because of its gauge invariance, because it is unambiguously defined from a physical observable, and because it is numerically stable. The oft used DR 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 tanβ, though related to a physical parameter, induces radiative corrections that are too large in many instances, and is therefore not recommended.