The existence of a light Higgs boson below the experimental upper bound mentioned above thus makes the latter possibility more plausible. Supersymmetry (SUSY) is a symmetry between bosons and fermions and imports chiral symmetry that protects fermion masses from divergence into scalar fields, thereby eliminating the quadratic divergence of scalar mass parameters. Since the principal origin of the naturalness problem in the Standard Model is the quadratic divergence of the Higgs mass parameter, its absence in the supersymmetric models allows us to push the cutoff up to a very high scale. This possibility, that the cutoff scale may be very high, provides us an exciting scenario, that all the weak scale parameters are determined directly from those at the very high scale where the supersymmetry is naturally understood in the context of supergravity. Stated conversely, we can probe the physics at the very high scale from the experiments at the weak scale.
Supersymmetry is, however, obviously broken, if it exists at all. Nevertheless, it should not arbitrarily be broken, as long as it is meant to solve the naturalness problem: only Soft Supersymmetry Braking (SSB) terms are allowed and the mass difference between any Standard Model particle and its superpartner should not exceed O(1) TeV. Most of more detailed analyses along this line put upper mass bounds on some SUSY particles that make their pair productions at the JLC possible. Turning our attention to the theoretical aspect of the above restriction to the SUSY breaking mechanism, we can classify phenomenologically viable models in terms of how the SSB takes place and how it is transmitted to our observable sector. Various SSB parameters at the high scale of SUSY breaking are determined by the choice of the SSB mechanism and the mediation mechanism.
In the early days of SUSY model building there existed essentially only one class of models, where the SSB is transmitted via gravity to the low energy world. While these models still being valid, the past few years changed the situation drastically and now we have a set of different models that include the aforementioned gravity-mediated models, Anomaly-Mediated SUSY Breaking (AMSB) models, Gauge-Mediated SUSY Breaking (GMSB) models, and models where the SSB mediation is dominated by gauginos. In any case, the low energy values of the SSB parameters are derived from those at the high scale by evolving them down to the weak scale via renormalization group equations. Consequently the SUSY particle masses and, in cases where mixing occurs, even their couplings are given in terms of the SSB parameters at the high scale, depending on the SSB mechanism. As we shall see in Chapter 3, once the first SUSY particle is found, we can carry out a consistent SUSY study program to step through the spectrum of SUSY particles and measure their properties in detail with the help of the clean environment and the powerful polarized beam that is available only at the e+e- linear colliders[19,20]. Once these low energy values of SUSY particle properties are measured, we can then in principle point towards the physics at the high scale and hence at the SUSY breaking mechanism.
The idea that the weak scale parameters are directly determined from a very high energy scale has naturally led us to the concept of the grand unified theory (GUT). It is well known that the three gauge coupling constants of the Standard Model do not unify, when extrapolated to the high scale using the Renormalization Group Evolution, while they do to a good approximation, if the Standard Model is supersymmetrized. The supersymmetric GUT models thus quantitatively explain the relative strengths of the three gauge coupling constants of the Standard Model. Furthermore, the baroque structure of the fermion quantum numbers in the Standard Model can be naturally embedded into a GUT gauge group, leading to the exact quantization of the electric charge and the precise cancellation of the anomalies. It is also worth mentioning that the heavy top quark naturally fits in the supersymmetric models, since its Yukawa coupling can drive the Higgs boson mass squared to negative at the weak scale thereby radiatively breaking the as needed.