THE WEAK-SCALE HIERARCHY AND DISCRETE SYMMETRIES

In the underlying Planck scale theory, we introduce a certain type of discrete symmetry, which potentially brings the stability of the weak- scale hierarchy under control. Under the discrete symmetry the mu-prob lem and the tadpole problem can be solved simultaneously without relyi ng on some fine-tuning of parameters. Instead, it is required that dou blet Higgs and color-triplet Higgs fields reside in different irreduci ble representations of the gauge symmetry group at the Planck scale an d that they have distinct charges of the discrete symmetry group.