In the absence of low-energy supersymmetry, a multiplicity of weak-scale
Higgs doublets would require additional fine-tunings unless they formed an
irreducible multiplet of a non-abelian symmetry. Remnants of such symmetry
typically render some Higgs fields stable, giving several dark matter particles
of various masses. The non-abelian symmetry also typically gives simple,
testable mass relations.Comment: Some comments added after Eqs. (2) and (12