# Is the big desert hypothesis a wilder assumption than the see-saw mechanism to explain neutrino masses?

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)!

• Right, @Dilaton. Dear Peter Shor, if you believe that the answer is something else than what I wrote, e.g. something written on a whining non-physicist's website, and you suffer from an unlimited belief that the website is right and that it is even a "physics blog", why don't you try to post it as an answer here? What is written on that website about the seesaw mechanism and big desert is as wrong as pretty much everything else written on that website. Without a coherent answer, your comments introduce nothing else than noise here. – Luboš Motl Jun 28 '13 at 16:21
• Lubos: the quote from Peter Woit here is saying that a calculation, based on the mass of the Higgs, that the universe is in a false vacuum and is thus unstable, should not be trusted because it relies on the big desert hypothesis. He is not saying anything about the seesaw mechanism. Your actual answer looks fine. – Peter Shor Jun 28 '13 at 16:24
• Dear @Peter, this comment has no direct relationship to the neutrino seesaw mechanism. Nevertheless, it's still bizarre, especially because the author of the phrase actually does believe - according to his comments everywhere on the blog - that there is no new physics at/right above the LHC, so it is correct to extrapolate the Standard Model to much higher energies. So which way it goes? He surely can't say that both options are absurd. Independently of that incoherent website, it is very plausible but uncertain that SM or MSSM or a similar simple theory holds up to very high energies. – Luboš Motl Jun 28 '13 at 17:48
• Incidentally, the new spectrum needed to restore the Higgs stability can't be just any new physics. It has to have couplings similar to the stop quark or higgsinos - i.e. supersymmetric particles, something that the favorite website of yours also humiliates and spits on everywhere. I am just saying that the assertions of the website are not only wrong but - in cases when the right answer is not known - they're internally inconsistent, too. One must have extremely poor intellectual standards if he or she finds these attitudes acceptable. – Luboš Motl Jun 28 '13 at 17:50
• The right conclusion is that the absence of SUSY below the Planck scale pretty much does imply that the Higgs potential destabilizes beneath the Planck scale. This is the important conclusion that your favorite quote from that website is trying to deny by spreading fog and injecting emotions into the discussion. – Luboš Motl Jun 28 '13 at 17:53

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.

• As I understand it, the see-saw mechanism assumes that there is an as-of-yet undiscovered neutrino which is very heavy, and the interaction between this neutrino and the known one makes the known one light. Are you saying that this see-saw mechanism puts absolutely no constraint on the mass of the heavy neutrinos? – Peter Shor Jun 28 '13 at 15:01
• No, I am surely not saying that. For the calculation to get the right mass of the visible neutrinos, of order $m_{EW}^2/m_{GUT}$, the heavy Majorana mass(es) has (have) to be around $m_{GUT}$. That's really the point that this numerology works. This numerology works not only with an explicit heavy right-handed neutrino but also with a generic dimension 5 operator suppressed by $1/m_{GUT}$ which may be generated in many ways. The big desert between the EW scale and the GUT scale - not including the end point themselves! - gives the simplest way to imagine the required spectrum. – Luboš Motl Jun 28 '13 at 16:17
• BTW there are three types of a seesaw mechanism, see motls.blogspot.com/2013/03/… for a discussion on that. Related articles on neutrinos and seesaw, see e.g. motls.blogspot.com/… – Luboš Motl Jun 28 '13 at 16:28
• Paraphrasing Heinrich Hertz : It is impossible to take part into physics SE with experiencing at times the strange feeling that the questions and answers somehow have a proper life, that they are smarter than we, smarter than their authors themselves, and that we somehow obtain from them more than was originally put into them … That's all for the _meta_comment! – laboussoleestmonpays Jun 28 '13 at 21:54

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 ;-)

• Hm I still dont quite understand why you introduce such philosophical issues (and the corresponding tag) into your good technical question ... – Dilaton Jul 13 '13 at 7:57
• Dear @Dilaton I thank you for your nice appraisal of the technical side of my question. As far as the epistemological side is concerned, I guess it is just my awkward, tentative (and possibly unnecessary) way to balance a pretty limited technical expertise :-) – laboussoleestmonpays Jul 13 '13 at 8:57