Disrupting the one-loop renormalization group invariant M/alpha in supersymmetry

It is well known that in low energy supersymmetry the ratio of the gaugino mass to the gauge coupling squared, M/alpha, is renormalization group invar iant to one loop. We present a systematic analysis of the corrections to th is ratio, including standard two-loop corrections from gauge and Yukawa cou plings, corrections due to an additional U(1)' gaugino, threshold correctio ns, superoblique corrections, corrections due to extra matter, GUT and Plan ck scale corrections, and "corrections" from messenger sectors with supersy mmetry breaking communicated via gauge mediation. We show that many of thes e effects induce corrections at the level of a few to tens of percent, but some could give much larger corrections, drastically disrupting the renorma lization group extrapolation of the ratio to higher scales. Our analysis is essentially model-independent, and therefore can be used to determine the ambiguities in extrapolating the ratio in any given model between the weak scale and higher scales. (C) 1998 Elsevier Science B.V.