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Supposing that the Standard Model is valid up to certain scale of energy $\Lambda$. Historically, the hierarchy problem was a motivation to propose new physics at TeV scale. No new physics is yet at hands at TeV scale in the LHC. Even SUSY is a framework quite model dependent that could rise up new physics until close enough to the Planck constant. My question is simple:

What are the arguments to guess/low/rise up where the energy scale is if it is BELOW Planck energy?

Bonus: comment how those arguments are biased by physicist "expectations" or "mood" in different theories. For instance, naturalness was one thought a good reason to TeV new physics. It is not so clear right now.

Bonus(II): where does the running of the gravitational constant enter into the game? Is it true that SUSY is capable to make the 4 couplings to meet at the same point (close to planck energy in most of the models?). That is an example.

Please, don't assume we want energy scale closer to the next experiments in order to have a job before of after the scientific AI menace comes.

riemannium
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  • Not to change the "guessed" scale of new physics to the current of projected colliders, experiments, in order to get "a job". I mean, is there any good argument or principle, independent of the energy scale accessible by colliders or detectors to really give a concrete value of the scale of new physics. Cheating: moving that scale close enough to accessible scales to justify those experiments without any reason. – riemannium Aug 12 '21 at 11:44
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    "What are the arguments to guess/low/rise up where the energy scale is if it is BELOW Planck energy?" This question implies that you do not understand what the Planck energy $is$. – Daddy Kropotkin Aug 12 '21 at 12:08

1 Answers1

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There are basically two guesses for $\Lambda$ to be below $M_{\rm Pl}$ that are based on some kind of physics argument.

  • $\Lambda \sim 1\ {\rm TeV}.$ The main reason for this guess, as you said, is the hierarchy problem. The Higgs mass receives corrections $\sim \Lambda^2$, so to avoid fine tuning, $\Lambda$ should be near the Higgs mass. As you know, this expectation does not seem to have been borne out by experiment (in retrospect, Arkhani-Hamed has been pointing out that if $\Lambda$ really was around a ${\rm TeV}$, there should have been signs at LEP, the precursor to the LHC). There are some other reasons people expected $\Lambda \sim 1\ {\rm TeV}$, for example the WIMP miracle, which argued that the abundance of dark matter would be explained if dark matter was a supersymmetric particle that decopuled from the thermal history of the universe at a temperature of around a ${\rm TeV}$. However, the WIMP miracle has become less appealing over time. There is a model of split supersymmetry due to Arkhani-Hamed and others which also addresses the hierarchy problem, but ends up with a scale $\Lambda \sim 100\ {\rm TeV}$.

  • $\Lambda \sim 10^{16}\ {\rm GeV}$. This is the "GUT" (Grand Unified Theory) scale. The main evidence for this, is that if you use the renormalization group to run the couplings of the strong, weak, and electromagnetic interactions, they approximately meet at this energy scale. The agreement is better if you assume supersymmetry "turns on" at around a ${\rm TeV}$. The "see-saw" mechanism for neutrino masses, also can explain the light masses of the neutrinos we observe, if the heavy right-handed neutrinos have a mass around this scale. However, the evidence is not iron clad -- three lines meeting near a point can be a coincidence, and the calculations are based on extrapolating the one-loop (or maybe two-loop?) renormalization group flow within the Standard Model. Higher loop corrections, or additional physics that could enter, all could change the RG flow.

There are other reasons to think there should be physics beyond the standard model (besides quantum gravity, which should become important around the Planck scale), but for which predicting a scale is much harder. The main candidates are dark matter, inflation, and dark energy.

Andrew
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