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In the SM with gauge group U(1)xSU(2)xSU(3), those factors are associated to the gauge bosons associated with a local symmetry and the Higgs field provides masses to the elementary fermions AND the W,Z bosons (the photon is inert) through SSB. My question is, the Higgs boson has (likely) a mass of about 127 GeV, what kind of symmetries prevent the Higgs to become very heavy through quantum radiative corrections? SUSY can make the work, but is there ANY clever alternative symmetry that protects the Higgs particle to become a superheavy particle via quantum corrections to the mass? I believe that the (minimal) Higgs boson has NO local symmetry associated to it, as far as I know...

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Some people have researched an `accidental' global symmetry. See Little Higgs: arxiv.org/abs/hep-ph/0512128 –  DJBunk Apr 16 '13 at 0:09
    
I have studied a little bit those models, and I can understand that the Higgs would be the "pseudo-Nambu-Goldstone" boson of some higher local symmetry hidden at high energy, where the symmetry would be restored and the Higgs field would become...Massless? What about CFT like the people working on unparticles/ungravity?Can conformal symmetry protect the higgs mass? –  riemannium Apr 16 '13 at 0:13
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You can also impose conformal symmetry of the vanilla standard model at the Planck scale and get the right Higgs mass from RG running if there are no new scales (apart from sterile neutrinos). Some refs: arxiv.org/abs/hep-th/0612165, arxiv.org/abs/1205.2893 –  Michael Brown Apr 16 '13 at 0:15
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