I've been reading about the higgs triviality bound (see for example here). It is discussed that the higgs self coupling at some energy scale becomes non-perturbative. If the higg's mass is above about 150 GeV, the coupling becomes non-perturbative after the Planck scale and this isn't of much physical interest in Nature.

Suppose however, that the higgs mass was above this scale. The claim is that we would need new physics at this scale. I'm confused as to why we would require new physics. Wouldn't the most likely scenario be that the higgs interactions are no longer perturbative and we have many new higg's bound states, in an analogous way to QCD?

  • $\begingroup$ Why is the word Nature uppercase? Do you mean the journal? [sorry, bad attempt at a joke] On a more serious note, hasn't the work at the LHC constrained the mass of the Higgs to some range? Does this range extend beyond 150 GeV/c$^{2}$? $\endgroup$ – honeste_vivere Jan 5 '15 at 18:27
  • $\begingroup$ Haha, I've seen people capatalize the word Nature for a while and I hopped on the trend. I'm not sure if its proper. The LHC has indeed heavily constrained the mass of the higgs, to something like 125+/-1. This is more of a hypothetical question or about any new scalars that my exist. $\endgroup$ – JeffDror Jan 5 '15 at 19:10

In the case of QCD there is asymptotic freedom, meaning that though the theory is strongly coupled at low energies (such that we still cannot analytically calculate how the atomic nucleus stays together) the coupling becomes less and less as we go to higher and higher energies. This means that the ultimate picture of the behavior of quarks is a weakly coupled theory where the quarks hardly interact with one another anymore.

In the case of the Higgs self coupling (or any other theory which becomes non-perturbative / strongly coupled / non-unitary) at higher energies it means that at higher energies the theory isn't suitable for any calculations (as opposed to QCD which still is in this case). This means that at higher energies certain calculations will give $\infty$ as an answer and no longer make any sense, we will find quantum mechanical probabilities that add op to more than $1$. Thus people hope (and historically this has happened a few times) that these theories that are non-unitary will become unitary again by introducing additional fields that will regulate the high energy behavior.

In the case of QCD this isn't a problem as we can go to higher energies where the theory does make sense. In the case of QED the self coupling of the electron was a problem, which was only solved by the additional interactions introduced in the Standard Model (though, that has some problems of its own as you pointed out)

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