Three of the leading figures in HEP theory have today or recently spoken about their current view of SUSY in light of the negative LHC results, here’s a report:

- At the IAS recently, Nima Arkani-Hamed spoke on The Inevitability of Physical Laws: Why the Higgs Has to Exist. Yuri Milner was in the audience, and I gather that this (and Maldacena’s recent similar talk) was intended to fulfill the promise of giving a public talk that came with their receipt of $3 million Fundamental Physics Prizes.
Both Arkani-Hamed and Maldacena talked not about their own work, but about the Higgs, with Maldacena emphasizing the importance of gauge symmetry, Arkani-Hamed the constraints imposed by unitarity and Lorentz invariance. At the end of his talk, Arkani-Hamed gave a big advertisement for SUSY, with a new and somewhat bizarre argument I hadn’t heard before. He argued that since QM + special relativity imply that elementary particles must have spin 0,1/2,1,3/2,2, and until recently 0 and 3/2 were missing, the fact that 0 (the Higgs) has now been seen implies (by the “totalitarian principle” that everything that can happen must happen) that the next thing to be discovered will require a spin 3/2 particle and this needs SUSY. Of the various weak arguments put forward for SUSY, this seems to me to be the weakest yet.

- At CERN today there was a 70th birthday celebration for Chris LLewellyn Smith. I didn’t watch John Ellis’s talk, but his slides are here. Evidently he argued that SUSY is not dead yet, pointing to the latest paper from the MasterCode collaboration. Their most recent CMSSM SUSY “predictions” have gluinos at either 2000 GeV (hard for the LHC to see at full energy after 2014) or 4000 GeV (impossible for the LHC ever to see).
No mention was made of the similar pre-LHC predictions (see here and here) which had the Higgs at around 113 GeV, gluinos at 700 GeV or so, and squarks lighter than this, all of which have been shown to be radically mistaken. For some perspective on this on an even longer time scale, take a look at this 1984 survey article, Supersymmetry – spectroscopy of the future? : or of the present?. It gives much the same enthusiastic motivation for SUSY that we still get in all SUSY talks, with Ellis optimistic that the latest data had hints of SUSY with sparticle masses around 40 GeV (“nicely compatible” with the recent discovery of a 40 GeV top quark…).

- Also speaking today was David Gross, and I did get a chance to watch his talk. He commented on Ellis’s claim that SUSY was not yet dead by noting “we see no signs of life either”, then went on to lay out two “extreme scenarios”. The pessimistic one would be nothing but the SM at LHC energies and no detection of dark matter. In that case, about SUSY he commented that it “could be that Nature does not take advantage of this”, which I think is the first time I’ve ever heard him raise this possibility. The optimistic scenario was the usual picture sold pre-LHC: detection of SUSY and dark matter, non-SM Higgs. Gross said that he’s an optimist, but gave no argument for the optimistic scenario beyond the one that it’s a good idea in life for a scientist to be an optimist.

**Update**: More at Nature about SUSY’s problems and quotes from its defenders.

**Update**: Over at the Simons Foundation web-site, there’s an excellent new article about the SUSY debate by Natalie Wolchover.

Spin 2 is missing also, as no one has seen a graviton.

@Roger,

The effects on a particle (change in position or spin) by a single graviton is indistinguishable from quantum fluctuations and since they have no electric charge do not interact with photons either.

How would one be able to observe a single graviton? (not gravitational waves).

Cheers, Paul.

I realize that no matter what I post about, people will want to discuss quantum gravity. Sorry though, that’s off topic. Find somewhere else to argue about the graviton.

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“He argued that since QM + special relativity imply that elementary particles must have spin 0,1/2,1,3/2,2, and until recently 0 and 3/2 were missing, the fact that 0 (the Higgs) has now been seen implies (by the ‘totalitarian principle’ that everything that can happen must happen) that the next thing to be discovered will require a spin 3/2 particle and this needs SUSY.”

Peter, I think you’re really twisting Arkani-Hamed’s words when you say this. He was not using the totalitarian principle to argue for SUSY; in fact, he never even mentioned the totalitarian principle. This phrase did appear on one of the slides that he skipped, but it looks like it was a slide about quantum mechanics, not SUSY.

His actual argument was something very different. He was saying that there are theoretical reasons why we can only discover elementary particles having spins 0, 1/2, 1, 3/2, and 2, and SUSY is required for spin 3/2. So because of theoretical constraints, SUSY is one of the very general ways in which new physics can show up in particle accelerators, and that’s why people are looking for it. In Arkani-Hamed’s own words,

“The reason why there is so much excitement about supersymmetry is—it doesn’t mean that it has to be right—it’s the last remaining thing. It’s the last thing that nature could do, in principle, that we haven’t seen it do. And we saw something fairly dramatic with the Higgs already. We saw the zero option used, so it’s not crazy that it’s going to come along with the whole thing, we’ll finally see the whole panoply actually used in the way nature works.”

At no point did he say that SUSY was definitely going to be discovered, or that it had to exist for theoretical reasons. All he said was “We haven’t seen it yet, but it’s something that we are looking for.”

Bob Jones,

Perhaps you’re right that the “totalitarian principle” business had nothing to do with the argument for SUSY, it was on a slide he didn’t have time to explain so one can’t be sure. But I don’t think I’m really misrepresenting his argument. I just looked at it again, and it’s clearly that spin 3/2 is the only non-observed spin on the list compatible with QM + special relativity and you need SUSY to get spin 3/2 consistently. Of course this is not an argument that you MUST have SUSY (none of the arguments for SUSY have ever been that you MUST have it), it’s an argument for likelihood of SUSY. And, if you ask me, a weaker one than any of the other standard ones for the likelihood of SUSY. Anyway, people interested are encouraged to see for themselves, it’s the last few minutes of the talk.

“Of course this is not an argument that you MUST have SUSY (none of the arguments for SUSY have ever been that you MUST have it), it’s an argument for likelihood of SUSY.”

Well, what you said was that, according to Arkani-Hamed, the discovery of the Higgs “implies” that the next thing to be discovered will be a spin 3/2 particle. When you say that a statement A implies another statement B, you mean that B necessarily follows from A. It doesn’t just mean the B is possible.

Also, I don’t think that the discovery of the Higgs makes it more likely that we’ll see a particle with spin 3/2. Arkani-Hamed is just saying it’s worth looking for because it’s one of the only ways for new particles to exist. The discovery of the Higgs shows that it’s reasonable to look for new particles whose spins lie in this small set of possibilities.

Bob Jones,

Yes, I was not using “implies” in the mathematician’s usage of logical implication, rather the colloquial usage of “suggests”. It didn’t occur to me that anyone would think this was a context where a claim of logical implication was being discussed. I did, I think accurately, describe it as an “advertisement”.

Also note that I wrote “the next thing to be discovered will require a spin 3/2 particle” (i.e. a form of SUSY with a spin 3/2 particle), not “the next thing to be discovered will be a spin 3/2 particle”. The particles SUSY enthusiasts expect to show up in LHC data don’t include the spin 3/2 one (the gravitino) itself.

Peter, I am a bit confused:

“you need SUSY to get spin 3/2 consistently”

then

“note that I wrote “the next thing to be discovered will require a spin 3/2 particle” (i.e. a form of SUSY with a spin 3/2 particle), not “the next thing to be discovered will be a spin 3/2 particle””

Excuse the naive question, but is SUSY the only way to have spin 3/2 particle in QM + special relativity ? (so, say, in QFT) ? I am not asking if this is the most common way explored by physicist, but if this is the unique way. If yes, then the argument does not seem so weak, at least it raises an interesting question: why spin 0, 1/2, 1 and – assuming graviton – 2, but no 3/2 ? Why a gap in the spectrum of the spin ?

martibal,

I’m no expert in the kind of argument that Arkani-Hamed was referring to claiming you need SUSY for spin 3/2, and don’t have time now to look this up, maybe someone else can get you a reference, and/or comment on the strength of such arguments.

I just don’t see the spin 3/2 “gap” as much of an argument. Part of this is a philosophical difference with Arkani-Hamed (I think the fields of the SM have specific and fundamental geometrical significance, with no particular reason to go to the kind of supergeometry where you get spin 3/2, whereas I would guess his is an effective field theory philosophy where the SM fields are nothing particularly fundamental). However, even if one accepts effective field theory philosophy, I still don’t think the argument is strong: the list of things we don’t understand about a more fundamental theory could include an explanation of why no spin 3/2.

Finally, all this has the problem that, unlike the hierarchy argument, it says nothing about the scale of SUSY breaking, so gives no indication of what energy scale one would see this spin 3/2 particle at. Arguments about how we must have SUSY, but which say nothing about its breaking just seem to me rather empty.

martibal,

The spin-3/2 analog of the Dirac equation is called the Rarita-Schwinger equation. Some quick looks around the web show (arXiv and Wiki) that when coupled to electromagnetism there are certain modes with propagate at faster than the speed of light.

On the other hand, supergravity definitely requires spin-3/2 fields and is consistent. Maybe someone can chime in some details about Vasiliev theory . . .

P

Peter (and anyone else),

I’m confused by the claim that you cannot have fields higher than spin 2. Obviously, there are composite particles with spin 5/2, 3, and so on to enormously higher values. I thought it was obvious that such particles could be represented by quantum fields.

Of course, their interactions are going to be a mess, but is there any objective criterion of simplicity that rules such interactions out of court?

I thought the whole idea of effective field theory was that the “real” underlying theory was God-only-knows-what, so that the “elementary” particles might be some weird incomprehensible sort of composites, but that our effective field theories nonetheless worked well enough at energies we can probe. And, so, there ought to be effective field theories to deal with the existing spin 5/2 or greater particles.

I assume I am missing some subtlety or fine distinction here: my education is so ancient as to pre-date the growth of the effective field theory idea (although I did take QFT from Steve Weinberg, whence I acquired the idea that *anything* can be represented by a quantum field!). I hope someone can fill me in on what I’m missing.

Dave Miller in Sacramento

@Dave Miller:

A more precise statement is that you can’t have such fields in a continuum QFT satisfying the conditions for the Coleman-Mandula theorem (which says basically that there would be so many conserved currents that the scattering matrix would have to be trivial). It’s fine to have such fields in effective field theories, and it’s fine to have them in QFTs where Coleman-Mandula doesn’t apply.

There is something soul-crushingly sad about watching SUSY theorists try to claim after the fact that the predicted the Higgs mass…

Noah,

Not really sure who you have in mind. The only one of the three theorists in the posting who had a precise Higgs prediction pre-LHC was Ellis, who was claiming that just about the LEP limit was the most likely value (that didn’t work out). Lots of SUSY theorists though have claimed vindication that the mass came out not so high that it couldn’t be reconciled with the MSSM.

If one takes a predictive model with free parameters and fits the indirect and direct constraints from experimental data, then one gets a chi squared for the range of these parameters, with a best fit point. With new data these fits can be updated to give a new best fit point.

When you do this exercise with the standard model before the LHC, the best fit point is under 100 GeV. With more data and direct searches, this best fit point moves up. With a lack of signal and a larger portion of the parameter space being constrained, you could also call that a desperate attempt to move the “prediction” to keep the theory alive.

But it’s not, it’s just updating the best fit of the free parameters, in the case of the standard model the only free parameter being one: the higgs mass. When gfitter kept updating their electroweak fits pre-Higgs discovery and their Higgs mass “predictions” kept moving up in light of LEP constraints, it wasn’t regarded as an arbitrary post-diction.

Doing these best fits for various minimal models of supersymmetry, with many more parameters of course, is no different. As more direct and indirect constraints are applied, the best fit points will shift, so the gluino mass will move up and so on. The best fit point by definition is the “more likely”, it’s just the minimum of the chi squared that comes out of the parameter fit to data, not a post-dicted “prediction” of where we will definitely find e.g. The gluino!

Before the higgs discovery the best fit to data for the one parameter model of a standard model Higgs was no different in spirit to the many-parameter fit of the CMSSM of e.g. Mastercode. How strongly one views these best fits as closing in on the gold coin hidden in the cake or evidence of a lack of gold coin is down to personal opinion, but if you belong in the latter camp it’s just dishonest to report these best fits as desperate attempts to keep a theory alive or change predictions, which then gets picked up by sensationalising science journalists and writers who get their information disproportionately from this blog.

jinb,

In the case of the Higgs, electroweak fits did a good job of, yes, predicting where the Higgs would be (the mass range it was likely to be in). If the Higgs had turned out to be at, say 300 GeV, they would tell us that there was something seriously wrong with the SM.

I’m not sure what the point of the SUSY fits now is. pre-LHC, they were advertised as predictions of SUSY spectra. What’s the lesson to be drawn from the identified likely regions being excluded (which is not what happened in the Higgs case)? Is it just that one needs to do new fits?

why in all the world would no susy and no DM be “pessimistic”?

i guess hep theorists are becoming lazy (or just old on average). the excitement of a 40 year old theory (SUSY) or a 80 year old (DM) being vindicated is not exactly the optimistic scenario i am dreaming of. as an optimist i hope that from experimental evidence we get some really new knowledge about a yet unknown principle of nature. susy and dm are actually really boring.

“it’s clearly that spin 3/2 is the only non-observed spin on the list compatible with QM + special relativity”

actually … for m=0 there is no half-integer restriction to the spin of a particle. why don’t we see any of these?

A.J.,

As I assume you (and everyone else) know, Coleman-Mandula rules out mixing internal and spacetime symmetries in non-trivial ways. (Of course, SUSY evades that with the anti-commuting, fermionic symmetries.)

But, I do not see how or why Colemna-Mandula rules out higher spin fields. In fact, the point I took away from my QFT class with Weinberg is that you can *always* construct such fields to represent composite systems. Of course, you may choose to build those fields out of “simpler” fields. Or not.

Now, maybe Steve was just way off base. And, I certainly may really be missing something. I’d appreciate it if anyone could tell me just where Steve (or perhaps my (mis)understanding of Steve) is wrong.

Thanks.

Dave

@Dave Miller:

The point is that C-M restricts the kinds of conserved currents you can have in the QFTs to which it applies. This is a problem if you want higher spin fields in your theory, because you’ll need to couple these fields to a current which C-M says can’t exist. Why? It’s a generalization of the argument that spin 1 particles need to couple to conserved currents. There are terms in the Fourier space propagator that don’t fall off fast enough with momentum and so will give divergences in loop integrals if they isn’t gotten rid of by coupling to a conserved current. This works OK for spin 1 theories; you can couple to a curren with 1 vector index, and the conserved charge will generate an internal symmetry. For spin 2, you are stuck coupling to the stress-energy current. Any other conserved tensor current would give a Noether charge that wasn’t energy-momentum; this is the argument that any ‘fundamental’ spin 2 particle must be a graviton. (For spin 3/2, you can couple to the super-current, if you have one.) For higher spin, you’d get conserved currents whose dotted and undotted indices number at least 3. C-M says there aren’t any.

My understanding is that this argument is due to Weinberg — at least the spin 2 part — but I don’t know the original literature.

There are ways around this argument, of course. You can work in a cut-off theory, and the loop integrals won’t get to cause trouble. This covers all the cases involved in nuclear physics. You can introduce towers of higher spin fields, like in string theory, and arrange for the bad terms terms in the propagators to all cancel out. You can work in theories with no mass gap, like CFTs, and then you’ll have a few more currents available.

Did David Gross leave out the detection on non-SUSY dark matter by the LHC? Does he believe this is unthinkable? It seems to me that it would be even more of a blow to SUSY than his worst-case scenario of not seeing anything. (Although it would presumably be great for high-energy physics in general.)

chris/Peter Shor,

To be fair to Gross, his discussion of the “optimistic scenario” was very short, and he clearly didn’t intend to characterize discovery of non-SUSY new physics at the LHC as not falling under this scenario. I’m pretty sure most SUSY advocates would drop it like a hot potato if there is solid new physics to investigate that clearly doesn’t fit at all in the SUSY framework.

Chris Llewellyn Smith obviously did some great work at CERN – their appreciation comes across clearly in the slides. More puzzling, though, is his subsequent career: he became Provost of University College London, but this was a poisoned chalice as it was in this capacity that he was responsible for cutting everyone’s budget. A palace coup followed and he was forced out. He then re-surfaced in something completely unrelated to High-Energy Physics: director of the UK fusion program. Don’t ask me how this happened: I was not even aware that he had an interest in the subject.

chris, its good to remember that there is absolutely ZERO evidence from astronomical observations alone that dark matter has electroweak interactions or anything to do with

TeV scale physics. (The only argument given is the “WIMP miracle”, but I think that is completely oversold and the limits from direct DM are already killing this strawman argument).

It could very well be all axions or all primordial black holes.

A.J.,

Thanks for going to the trouble to fill in the details I was asking for — I appreciate it.

If you or anyone can remember any references that explain all this in more detail, I’d be interested in seeing the references. I’ll check and see if I can find any of Steve’s stuff that goes into it — this whole issue does seem to be something that has preoccupied him off and on over the decades. (Here is a popular article where he discusses his interest in the composite vs. elementary particle issue over the years: http://www.slac.stanford.edu/pubs/beamline/27/1/27-1-weinberg.pdf.)

Thanks again for your replies.

Dave

Weinberg’s original paper showing that massless spin 2 particles can only couple to the energy-momentum tensor is:

S. Weinberg, “Photons and Gravitons in S-Matrix Theory: Derivation of Charge Conservation and Equality of Gravitational and Inertial Mass,” Phys. Rev. 135 (1964) B1049-B1056.

The argument applies only to couplings that result in Coulomb-like or Newton-like long-range forces, and Weinberg points out that under similar assumptions, there is nothing for massless particles of integer spin 3 or higher to couple to.

“I’m pretty sure most SUSY advocates would drop it like a hot potato if there is solid new physics to investigate that clearly doesn’t fit at all in the SUSY framework.”

And what sort of new physics that one can see at the LHC that could not possibly fit a SUSY framework?

Peter, as you claim, if this 3/2 argument is the weakest of all the arguments for susy, then that actually makes the sum total of the arguments for susy very very strong, i.e., if this is, as you claim, the “lower bound” on the quality of susy arguments, then that is quite impressive, since by definition, all other arguments must be even a lot stronger. If on the other hand this was the “upper bound” on the quality of susy arguments, then one might think the remaining arguments to be pretty weak.

In summary, I am quite surprised to see Peter to be so supportive of susy for a change.

Bob,

I described the 3/2 hole as the weakest of various weak arguments. I suppose how one orders in strength a list of not very good arguments is to a large degree a matter of taste. One reason for putting this in the weaker category is that it says nothing about the energy scale of SUSY breaking (unlike the hierarchy, wimp miracle, coupling constant unification arguments, which require low scale SUSY breaking and supposedly explain something about the world we see).

Actually I think the 3/2 hole argument is just a variant of the standard argument “SUSY is a consistent extension of known symmetries and more symmetry is good and will be used by nature”, but weaker (so there’s a 3/2 hole? so what?).

Hello Peter,

As a field theory based on the Poincare-group (like the Standard Model) doesn’t allow a well behaved spin 3/2 particle, it is actually the absence of a spin 3/2 particle in Nature that confirms that the fundamentals on which the Standard Model has been constructed are sound!

Peter,

“unlike the hierarchy, wimp miracle, coupling constant unification arguments, which require low scale SUSY breaking”

Nima and Savas argued in hep-th/0405159, the original split supersymmetry article, that split susy is consistent with coupling constant unification, because the heavy squarks and sleptons come in SU(5) multiplets, and do not affect unification at one-loop order. The second Higgs doublet of the SSM is also heavy, and they claimed on page 7 that its absence might actually improve the unification prediction over the SSM when two-loop contributions are included.

Chris,

Yes, but the point of split SUSY is that it keeps the gauginos at TeV-scale in order to preserve coupling constant unification, and I’d describe that as “low scale SUSY breaking”. If you give up on low scale SUSY breaking completely (and do “supersplit supersymmetry”, which is an April Fool’s joke, not a theory…) you lose coupling constant unification. And, with split SUSY, you already lost the explanation of the supposed hierarchy problem.

Hi Peter

sorry to contradict you but you can have a nice SO(10) unification without any need of supersymmetry. And please consider that SO(10) helps to understand neutrinos masses, the only solid fact on “beyond the standard model physics”; on the contrary, SU(5) happilies marry with supersymmetry, but doesn’t help with neutrino masses.

fuzzy,

I didn’t really intend to say anything one way or another about non-SUSY theories, the comment was about different SUSY variants. But, is there really still a viable SO(10) GUT that doesn’t have problems with proton decay? My impression was that both SU(5) and SO(10) GUTs had such problems, worse in the non-susy case, but I haven’t followed this recently.

hi peter

proton decay is not a problem is the only experimental test. i know we are theorists but should agree on the definition what “physics” is don’t you think so? in my view, the problem is that the efforts put in supersymmetry and strings stopped the progresses in gauge theories — the only successful thing we have — so i hope that sooner or later we will come back to discuss this. anyhow, putting aside these general issues, some work is still being done on so(10); curiously even the simplest theories are not fully analyzed see e.g., http://prd.aps.org/abstract/PRD/v85/i9/e095014