Will discrete symmetries help solve the hierarchy problem ?
  We find that massless Higgs doublets at the GUT scale can be the natural result of a discrete symmetry. Such a mechanism does not require elaborate fine tuning or complicated particle content. The same discrete symmetry will also protect against proton decay and flavor changing neutral currents. However, this mechanism always predicts non-minimal standard models. An explicit example of how this mechanism works is also included. 
Meng Y. Wang and Eric D. Carlson (Lyman Laboratory of Physics, Harvard   University Cambridge, MA 02138)