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The one is supersymmetry. This gives to each particle we already know a heavier superpartner, which has the property to cancel the contribution of its original particle in these loops (for physicists not connected to the matter, it makes a boson partner for every fermion and vice versa. In Feynman diagramms fermions come in with a negative sign, bosons with a positive, so the superpartners cancel their normal partners). The proposed particle I wrote in the diary to catlyse fusion is the stau, the superpartner of an even much heavier partner of the electron than the muon. In some parameter space it can be realively long living.
The other is some variation of 'techni color' or 'warped extra dimensions'. This is in general the more 'natural' solution of the problem, but even more than in the case of supersymmetry one would have expected to find deviations of the standard model about 20 years ago.
The good things about the LHC is, that we really enter the region in which these models have to exist, if they should help to solve any problem. Der Amerikaner ist die Orchidee unter den MenschenVolker Pispers
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