Conformal Solution
Without supersymmetry, a solution to the hierarchy problem has been proposed using just the Standard Model. The idea can be traced back to the fact that the term in Higgs field that produces the uncontrolled quadratic correction upon renormalization is the quadratic one. So, if the Higgs field had no mass term no hierarchy problem arises. But, missing a quadratic term in the Higgs field, one must find a way to recover the breaking of electroweak symmetry through a non-null vacuum expectation value. This can be obtained using the Weinberg-Coleman mechanism with terms in the Higgs potential arising from quantum corrections. Mass obtained in this way is far too small with respect to what is seen in accelerator facilities and so a conformal Standard Model needs more than one Higgs particle. This proposal has been put forward in 2006 by Krzysztof Meissner and Hermann Nicolai and is currently under scrutiny. But if no further excitation beyond the one seen so far at LHC would be observed, this model should have to be abandoned.
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