Hierarchies in Grand Unification

The theoretical aspiration of unifying all interactions through the mechanism of a spontaneously broke gauge symmetry received some encouragement recently with the discovery of the W('(+OR-)) and Z(DEGREES) electroweak bosons predicted in the Glashow-Weinberg-Salam model of spontaneously broken SU(,L)(2) x U(,Y)(2). However the null results from proton decay experiments have dampened the hope that SU(5) is the correct model and placed some doubt on whether experimental evidence for grand unification can ever be seen. This situation has prompted us to look for other tests of grand unification and in particular to examine the possibility and testability of models larger than SU(5) which can have intermediate scales of symmetry breaking. We have studied some low energy models containing two light Z bosons and confronted them with the electroweak neutral current data to determine whether or not they can consistently fit it and if so what it implies for the masses of the Z bosons. The electroweak neutral currents also provide us with information on the low energy values of the gauge couplings which we used to establish limits on the hierarchy scales in an SO(10) model. Finally we discuss the theoretical fine tuning problem that arises in any model with a large scale hierarchy. The problem lies in the Higgs sector and can be related to the existence of quadratic divergences in the Higgs mass parameter. A "naturalness" criterion for a grand unified theory requires the absence of these quadratic divergences in order to make the hierarchy stable under radiative corrections. We show in a large class of renormalizable quantum field theories that if there occurs a cancellation of quadratic divergences for the scalar mass terms, then the only interaction structure allowed is that of supersymmetry. Thus the only "natural" solution to the gauge hierarchy problem must be a softly broken supersymmetry with superpartners of the known particles expected to have masses less than 1 TeV.