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When model building we don't want to introduce any new scales into our theory. We usually try to have new particles at the Higgs (TeV) scale (to solve the hierarchy problem), at the GUT scale, or at the Planck scale.

However, if the Higgs VEV already gives us a new scale, why would there not be new particles at some intermediate scale, for example say at $10^{5}$ TeV? In other words, what is unnatural about adding in new scales beyond the 3 that we are used to?

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Actually, the Higgs scale is not the TeV scale. The Higgs scale is the scale of electroweak symmetry breaking, i.e. $\mathcal O(100 \mathrm{GeV})$.

The Terascale comes into play along with the Higgs, as supersymetry - the most popular extensions of the Standard Model - would actually like a small Higgs mass, much smaller than its measured value ($< M_Z$ to be more precise). In order to have a Higgs mass at $125$ GeV, we need supersymmetry breaking parameters to be on the order of TeV at least (disregarding extremely specific scenarios). Higher scale supersymmetry is still possible, but would not be as attractive from a more fundamental point of view.

There are also other effects, like the running of the strong coupling constant that could also hint at new physics, if we found a deviation at higher energies. Or gain further information on the viability of ideas such as Grand Unification.

Most importantly, with the LHC we can actually measure at the TeV scale, i.e. models and ideas taking place there have a realistic chance of getting verified or falsified in the forseeable future. I think that's the main reason, why Terascale physics is so important right now.

Edit - for more information: Fundamentally, there is nothing wrong with having many scales. Still, it would be hard to justify a world with effects at many different fundamental scales. The scale at $E \sim 0$ comes free, as this is the only energy that is fundamentally different from all others. This scale includes electromagnetic and strong force effects, i.e. all atomic and most nuclear dynamics (as they arise from interactions with massless force carriers). Then, we have one other scale for free, just because we see that there IS mass in the world. But looking at particle physics and gravity, we already have two: The electroweak scale $E \sim 100$ GeV and the Planck scale $E \sim 10^{19}$GeV. Quantum corrections want to equalize the scales, unless there is a symmetry protecting the quantity in question. That's one of the reasons supersymmetry is so popular: It adds a symmetry to protect the Higgs mass (which should be of the order of the Planck scale otherwise). Often, we theorists add the GUT scale $E \sim 10^{15}$ GeV to the picture as an intermediate scale, since the three forces of the Standard Model are (approximately) equally strong there. Then we already have four scales (of which we need to explain two). Now add the Terascale for supersymmetry breaking and we have five (three to explain). This is unsatisfactory, but alas, it's the best we can do for now.

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  • $\begingroup$ I would say that there was only 1 scale, the electroweak, that we need to explain. Why do you say 2? Furthermore, with SUSY you say now there is an extra scale. That is basically the mu-problem, but it is not so bad as other hierachies, eg mu is stable under corrections, and can be solved by eg NMSSM or Giudice Maseiri mechanism. $\endgroup$
    – innisfree
    Commented Mar 14, 2014 at 15:55
  • $\begingroup$ Indeed, the GUT scale comes for free if one assumes a unifying gauge group with the matter content of the SM. Besides ameliorating the little hierarchy problem, there is however no particular reason why NP effects should happen at the Terascale. $\endgroup$
    – Neuneck
    Commented Mar 15, 2014 at 10:45
  • $\begingroup$ @Neuneck: So if I understand correctly you state that we don't add extra scales because there is no need for them - essentially an Ocaam's razor arguement. Each other scale that we have has definite meaning. I see what you are saying but doesn't that seem if nothing else, questionable. Why do we believe these scales are so sacred? $\endgroup$
    – JeffDror
    Commented Mar 15, 2014 at 17:06
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    $\begingroup$ Because we DO observe phenomena related to these scales. The Planck scale is related to gravity, the GUT scale to the coupling constants, the weak scale to the Higgs vev or Z Mass. If you develop a theory that dynamically explains the emergence of the ratio of two of the above, that would be a big deal. (Note there is also the QCD RG-invariant scale $\Lambda$, which CAN be explained dynamically and which I therefore do not consider fundamental, but emergent). If one believes in a theory of everything, one should also believe in a universal energy scale fixing all scales through ratios. $\endgroup$
    – Neuneck
    Commented Mar 17, 2014 at 7:04
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If you want the new physics to solve the hierarchy problem, it's best if it is close to the weak scale, or else you will be left with a residual little hierarchy.

You are describing the "big desert" between the weak and GUT scales. I think it was motivated by the idea that SUSY lived at the weak scale, solving the hierarchy problem and insuring gauge coupling unification. Any physics between those scales would be unnecessary, could spoil unification or induce FCNC and proton decay.

I don't think the big desert hypothesis is particularly compelling, especially in light of the LHC results, but it is plausible.

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  • $\begingroup$ From my experience with model building people avoid introducing new scales at all costs. If SUSY is not found at the TeV scale then should we change our approach to model building? $\endgroup$
    – JeffDror
    Commented Mar 15, 2014 at 17:08
  • $\begingroup$ The answer is unclear, but will probably become clearer over the next year or two. In my opinion, naturalness problems need a physical explanation. There are many who will say, "hey naturalness isn't a physical law, it's just a failed heuristic SUSY adherents cooked up. Let's forget it. The SM is just fine." $\endgroup$
    – innisfree
    Commented Mar 15, 2014 at 18:01

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