Supersymmetric Electroweak Renormalization of the Z-Width in the MSSM (I)

Within the framework of the MSSM, we compute the complete set of electroweak one-loop supersymmetric quantum effects on the width ${\mathrm{\Gamma }}_Z$ of the $Z$-boson in the on-shell renormalization scheme. Numerical analyses of the corrections to the various partial widths into leptons and quarks are presented. On general grounds, the average size of the electroweak SUSY corrections to ${\mathrm{\Gamma }}_Z$ may well saturate the level of the present theoretical uncertainties, even if considering the full supersymmetric spectrum lying in the neighbourhood of the unaccessible LEP 200 range. Remarkably enough, for the present values of the top quark mass, the electroweak SUSY effects could be, globally, very close or even bigger than the electroweak SM corrections, but opposite in sign. Therefore, in the absence of theoretical errors, there are large regions of parameter space where one could find that, effectively, the electroweak SM corrections are missing'', or even having the wrong’’ sign. This should be helpful in discriminating between the SM and the MSSM. However, an accurate prediction of the electroweak quantum effects on ${\mathrm{\Gamma }}_Z$ will only be possible, if $\mathrm{\Delta }r$ and ${\alpha }_s$ are pinned down in the future with enough precision.