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Sometimes I see comments about the big desert hypothesis that I don't understand. For instance in a famous blog :

...This is based on a renormalization group calculation extrapolating the Higgs effective potential to its value at energies many many orders of magnitude above LHC energies. To believe the result you have to believe that there is no new physics and we completely understand everything exactly up to scales like the GUT or Planck scale. Fan of the [Standard Model] that I am, that’s too much for even me to swallow as plausible...

and recently in an interesting answer to another question I asked on physics.stackexchange

This is a very strong assumption (although certainly not unknown in particle physics): They are assuming that there is no new physics across 16 orders of magnitude.

I wonder if this kind of feeling about this hypothesis is common because I've never found similar comments about the see-saw mechanism which, as far as I understand it of course, makes a connection between grand unification or Planck scale and neutrino sector energies (a much larger leap for a physicist I guess ;-)

As far as I am concerned I am a Standard Model (and effective (and noncommutative) theories) enthousiast! I imagine that its validity could go from $10^{-18}$eV (upper limit of the photon mass) to $10^{+12}$eV (LHC energy), these are 30 orders of magnitude on the energy scale. Then the 16 ones of the big desert hypothesis from TeV scale to Planck scale are just one giant step further, half long forward so to speak. I could be wrong of course but very naively I take inspiration from the past when chemists were bold enough to imagine atoms and physicists like Rayleigh clever enough to evaluate molecular size extrapolating the validity of euclidean 3D geometry from human scale (cubic centimeter) to oil molecule scale ($10^{-21}$? cubic centimeter)!

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laboussoleestmonpays
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2 Answers2

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First of all, the big desert hypothesis isn't in contradiction with – isn't a competitor of – the seesaw mechanism for neutrino masses. Quite on the contrary, assuming a big desert between the electroweak scale and the GUT scale is the most natural way to be sure that the small seesaw terms in the neutrino masses are the dominant ones that matter. The seesaw terms may arise from right-handed neutrinos whose Majorana masses are near the GUT scale; or from any other relevant dynamics at the GUT scale, too.

Second of all, the big desert isn't quite necessary for the seesaw mechanism to work, either. If there's some physics at the intermediate scales, one still has to discuss the character of this physics. For some sufficiently decoupled or peaceful physics, one may still guarantee that the leading terms in the neutrino masses arise from a seesaw mechanism.

Third, the GUT scale – whenever it makes sense to talk about it – is always much closer to the Planck scale than the LHC scale. At least in models people consider, a GUT scale that would be vastly smaller than the Planck scale – by more than a factor of 1,000 or so – would have at least one of the two vices: 1) a rapid proton decay incompatible with the observations, 2) insufficient running to actually achieve gauge coupling unification.

Fourth, eV is the "basic" unit in the sense that it has no prefixes indicating any multiples or fractions but in particle physics, people really use GeV as the main unit – much like kg is the main SI unit of mass despite its being a multiple of the prefix-free unit, one gram.

Fifth, more importantly, there is no quite scientific way to compare the likelihood of two qualitatively different scenarios for physics none of which is really excluded by a solid argument. Both particle physics (we may mean either effective quantum field theories or string theory vacua that become equivalent to them at long distances) with a big desert and particle physics with lots of intermediate layers of dynamics are viable at this point. I would personally bet on the big desert (between SUSY near the electroweak scale and the Planck scale) because it's economic and nontrivially agrees with the coupling unification. But this preference is far from absolute, it's dictated by some subjective feelings and priors, and once these arguments are abandoned, there are pretty much no other viable arguments and having no physics in between may be viewed as rather unlikely.

Luboš Motl
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I want to thank Lubos Motl to answer the question with his well-known technical and pedagogical expertise but I would like also to underline the epistemological aspect or heuristic issue at stake in my question.

I think, like Lubos, that the big desert is just a simple and natural hypothesis one can make in an effective theory perspective. I don’t see any reason not to test the observational consistency of a mathematically coherent theory injecting it in the wonderful renormalization group machinery and using a simple hypothesis. As far as I understand it, this approach is nothing but natural reductionist philosophy made quantitative thanks to the insights of people like Wilson and ‘t Hooft, some of our finest Standard Model Heroes ;-)

laboussoleestmonpays
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