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I think you still need a Higgs-like state (although not necessarily the Standard Model Higgs; dynamical symmetry breaking through a technirho mechanism will suffice) to preserve unitarity in the electroweak sector.

If you keep talking dirty like that, I'm liable to get aroused! Stop before I can't control myself any longer!

Seriously, I had never heard about this idea of mass being attributed to a "mystery dimension" -- it's very intriguing and has a fascinating, almost intuitive appeal. Thanks for sharing it with us Philistines.