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Light Threshold Effects in Supersymmetric Grand Unified Theories

Supersymmetric Grand Unified Theories have a rich spectrum of particles barely heavier than the intermediate vector bosons. As their non-supersymmetric counterparts, they lead to many relations among low energy observables. But the precise form of the predictions is modified by the extended spectrum. If the masses of these new particles are comparable to $M_Z$, the standard computation of their effect becomes inaccurate. We present a detail discussion of the correct procedure, and carry out the relevant computations to one loop order. The procedure we propose has the advantage over other existing methods that two-loop running of gauge couplings can be incorporated readily and consistently. Attention is paid to the special treatment that the top and Higgs particles must receive. The size of the effect is explored for a range of parameters in the minimal supersymmetric $SU(5)$ grand-unified theory with radiative breaking. It is found that the naive (leading-log) computation can be fairly inaccurate.