While reading up on hierarchy problems in particle physics (wikipedia), I stumbled onto the statement that in the Standard Model, there is no hierarchy problem (or at least it cannot be formulated) since the Higgs mass can not be calculated.

I don't understand what exactly is meant by this. In what sense can you “calculate the mass of the particle”? I assume implied here is the bare mass.

Why if at all, are we able to calculate the bare mass of, say, an electron but not the Higgs? Would we not by the same token need to know all interactions at higher energies to compute radiative corrections to electron masses?

Maybe my question could be entirely reduced to why hierarchy problems show up in extensions to the SM only for the Higgs and not for other SM particles.

Edit: I do realise that my question contains a spiral of questions resulting from basic confusions but I'd much appreciate to be pushed in the right direction.

Edit 2: I grew to believe that Wikipedia is misleading and the essential point is that scalar particles lead to quadratic divergences which make the Higgs mass extremely sensitive to the cut-off energy scale. I think the problem “cannot be formulated in the SM”, since then there would be no cut-off, which is a ridiculous statement in itself.

  • $\begingroup$ all the masses in the standard model are "axiomatic", i.e. measured and assumed as elementary, not just the Higgs.en.wikipedia.org/wiki/Elementary_particle . I think the emphasis on the Higgs comes because maybe in extensions of the SM the mass of the Higgs might be calculable. $\endgroup$ – anna v Apr 22 '19 at 18:58
  • $\begingroup$ As far as I know the reason that there is no hierarchy problem in the SM is that there only is one scale namely the Higgs vev so there is no hierarchy between different scales. $\endgroup$ – Katermickie Apr 22 '19 at 22:08
  • $\begingroup$ syymmetries.blogspot.com/2017/06/… $\endgroup$ – Mitchell Porter Apr 24 '19 at 20:57

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