Of Particular Significance

Where Stands Supersymmetry (as of 4/2012)?

Matt Strassler [April 24, 2012]

[A Heads Up: I’m giving a public lecture about the LHC on Saturday, April 28th, 1 p.m. New York time/10 a.m. Pacific, through the MICA Popular Talks series, held online at the Large Auditorium on StellaNova, Second Life; should you miss it, both audio and slides will be posted for you to look at later.]

Is supersymmetry, as a symmetry that might explain some of the puzzling aspects of particle physics at the energy scales accessible to the Large Hadron Collider [LHC], ruled out yet? If the only thing you’re interested in is the answer to precisely that question, let me not waste your time: the answer is “not yet”. But a more interesting answer is that many simple variants of supersymmetry are either ruled out or near death.

Still, the problem with supersymmetry — and indeed with any really good idea, such as extra dimensions, or a composite Higgs particle — is that such a basic idea typically can be realized in many different ways. Pizza is a great idea too, but there are a million ways to make one, so you can’t conclude that nobody makes pizza in town just because you can’t smell tomatoes. Similarly, to rule out supersymmetry as an idea, you can’t be satisfied by ruling out the most popular forms of supersymmetry that theorists have invented; you have to rule out all its possible variants.  This will take a while, probably a decade.

That said, many of the simplest and popular variants of supersymmetry no longer work very well or at all. This is because of two things:

No Superpartners Have Shown Up Yet

The reason to think superpartner particles might show up at the LHC is that supersymmetry offers a possible solution to the hierarchy problem — the puzzle of why there is such a huge ratio between the extreme weakness of gravity and the relatively powerful force of electromagnetism (and the similarly powerful weak and strong nuclear forces.) This ratio permits you to raise your arm effortlessly, using electrical processes in your nerves and muscles, despite the gravitational pull of the entire earth. The problem with this hierarchy isn’t its presence by itself, but that theorists have a difficult time finding equations that allow for its presence. (More precisely, they have a difficult time arranging for it while simultaneously obtaining the large mass of the top quark and avoiding big increases in the rates for rare processes such as this one.) This is because effects of virtual particles (which aren’t really particles at all, but more general quantum-mechanical disturbances in the fields of nature) have a big impact on the physics that determines how the Higgs field becomes non-zero on average. If you take just the known particles and forces and study their quantum effects, you’d expect these effects to force the Higgs field’s average value to become EITHER

  • zero (and thus making the W and Z particles and matter particles massless), OR
  • very, very large, something around 1,000,000,000,000,000,000 GeV (and thus making the W and Z particles and matter particles millions of billions of times more massive than they are.)

But in a supersymmetric theory, the virtual-particle effects of the known fields on the Higgs mostly cancel against similar effects from superpartner fields, as long as there is one superpartner field (and its particle) for each known field (and its particle), and as long as those superpartner particles have masses not much more than 1 TeV/c2.

Fig. 1: ATLAS results from supersymmetry searches for high-energy quarks, antiquarks or gluons plus signs of invisible particles (`missing energy'). On a plot of squark mass versus gluino mass, everything below the red line is excluded by the 2011 ATLAS data. The yellow gives the results from mid-summer 2011, showing how rapidly the search has proceeded. Many assumptions go into this plot; for more information go to https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/CONFNOTES/ATLAS-CONF-2012-033/

For this reason, not finding superpartner particles below 1 TeV/c2 is disappointing to a supersymmetry advocate, because in most of the simplest variants of supersymmetry they should have shown up by now.

But there are big caveats to discuss at this point.

As I have explained in previous posts and articles from last summer, several assumptions go into the standard searches for superpartner particles. As of last summer, all the searches that had been done relied strongly upon these assumptions; that is why I said vehemently back then that supersymmetry was in no way ruled out, contradicting my experimental colleague John Conway’s post on the matter. Well, the very fact that so many additional searches have been done by ATLAS and CMS since the summer clearly indicates who was correct on that little teapot tempest! 🙂 And yet, the number and the range of the newer searches is still not enough.  While some of the assumptions that go into the standard searches have been partially relaxed, an exhaustive set of searches has still not been carried out. Even for nearly standard variants of supersymmetry, relaxing even one of those three assumptions, much less two of them, can easily allow superpartners of the quarks and gluons to have been missed so far. [I gave you specific examples back in the summer I am pretty sure still generally hold at the present time.]  As I’ve been arguing since 2006, we’ll really have to be a lot more thorough, both on the experimental and on the theoretical side, before we can conclude that even the standard variants of supersymmetry are completely excluded. I hope that in late 2012 or early 2013 we’ll start seeing the remaining gaps start to close, but I suspect it will be more like late 2013 or early 2014 before this happens.  [Don’t worry, I’ll let you know.]

Fig. 2: CMS exclusions on a variant of supersymmetry that produces photons and signs of invisible particles, along perhaps with high-energy jets. Note the axes are reversed compared to Figure 1. Many assumptions go into this plot; for more information see https://twiki.cern.ch/twiki/bin/view/CMSPublic/PhysicsResultsSUS12001

But if instead one does make the standard assumptions,

  1. in any process, the number of superpartners can only change by an even number;
  2. the lightest superpartner [which is stable, by assumption 1]  is a superpartner of a particle we know (and therefore, to avoid conflict with other data, an undetectable neutralino or sneutrino);
  3. the superpartners that are affected by the strong nuclear force are significantly heavier than the other superpartners of known particles,

and asks what we now know about variants of supersymmetry that satisfy these assumption, one realizes that we are now forced to consider some significant twists on the conventional thinking.  Along these lines, it was observed over 15 years ago (maybe much more?) that there are certain superpartner particles that are more important for the hierarchy problem than the others. These are the superpartners of the heaviest known particles, which are the ones that interact most strongly with the Higgs particle: the partner of the top quark (called the “top squark”) and the partners of the W, Z, and Higgs particles (the “neutralinos” and “charginos”). And these particles are not produced nearly as often as the superpartners of the particles that are most abundant in the colliding protons: the gluons and the up and down quarks (and anti-quarks). Existing searches for supersymmetry have indeed ruled out the presence of lightweight gluinos and up and down squarks, but this is not true for the most important superpartners. It is still possible, given what we currently know, that nature has a top squark that is lighter than the top quark!  It has not been excluded experimentally yet.   And neutralinos and charginos could also still be quite light (not much above 100 GeV/c2) and so far have escaped detection.

It has long been known that ruling out the presence of top squarks and of neutralinos and charginos would be one of the significant challenges for the LHC experiments. The signals of these superpartner particles are small, and there are very large backgrounds from other processes, arising from the known particles, that mimic these signals. The year 2012 will see significant efforts to search for signs of these (or similar) particles, and to either discover or exclude them up to much higher masses than has been achieved up to now. But to do this well will involve very hard and detailed work on the part of both theorists and experimentalists.

A Higgs Particle, A Tad Too Heavy, May Be Showing Up

Meanwhile, if the preliminary evidence of a Higgs particle at 125 GeV/c2 from the ATLAS and CMS experiments at the LHC (see this post and this one for the latest Higgs news) turns out to be for real, that too puts important constraints on supersymmetry. (There are at least five Higgs particles in a supersymmetric theory, three electrically neutral and two of them charged.  But in many variants of supersymmetry, only one Higgs particle is particularly light. This one often appears rather like a Standard Model Higgs particle, until one studies it in detail, and quite possibly this is what the LHC experiments are starting to observe.)  The reason is that naively supersymmetry would not permit the lightest Higgs particle to be heavier than the Z particle, which has a mass of 91 GeV/c2. This is because in the simplest variants of supersymmetry the strength of the weak nuclear force sets both the Z particle mass and the Higgs particle mass. This is not at all true in the Standard Model (the equations which govern the behavior of the known particles, without any superpartner particles.) Because of large quantum corrections (specifically, effects of virtual particles, especially of the top quark field and its superpartner, the top squark field, on the Higgs field), the Higgs particle’s mass can move above this naive limit. Still, in the simplest supersymmetric models it is difficult for these effects to pull the Higgs mass above 115 GeV/c2, and very difficult for them to pull it above 120. To get to 125 requires squeezing or modifying the theory.

Fig. 3: Assuming the Higgs mass is at 125 GeV, contours of the ``A-term'' parameter (which measures how strongly the two top squarks are mixed) as a function of the heavier (vertical) and lighter (horizontal) top squark's mass. The A-term must be larger than 1 TeV, but the lighter top squark could be as low as 200 GeV. The dark gray region cannot have a Higgs mass at 125; the light gray region has the squark masses in the wrong order. Taken from Draper et al., 2011, http://arxiv.org/abs/arXiv:1112.3068

Within the minimal form of supersymmetry — one superpartner for each known particle, along with five Higgs particles and their superpartners, and nothing else — the only way to get a large Higgs particle mass is to pull the masses of top squarks way up to 5 TeV/c (reintroducing a limited form of the hierarchy problem —  if the top squarks are so heavy, why is the Higgs field’s average value neither zero nor several TeV?) or to allow the two top squarks (yes there are actually two, because of how the top quark is assembled from a top-right field and a top-left) to mix strongly with each other, allowing one of the top squarks to be very lightweight.

On the theoretical side,  the need for large mixing has important implications.  The parameter which determines mixing (historically called an “A-term”, a supersymmetry-violating interaction between the Higgs field and the two top squark fields for which there is no Higgs-quark-antiquark counterpart) must be very large, as shown in Figure 3.  [Experts; note that tan beta must also be reasonably large to get the Higgs mass to 125, so the difference between Xt and At is probably small.] Some variants of supersymmetry cannot easily accommodate either a large A-term or very large top squark masses, and so, if the Higgs is really there at 125 GeV/c2, those variants are ruled out.

On the experimental side, this argument, too, would lead one to think that looking for top squarks, with potentially low masses, is important for 2012. And because virtual gluinos contribute to the top squark mass, one would also expect they too would not be extremely heavy, and would likely also be observable this year.

There are ways around this line of argument.

  • If there is an additional as-yet unknown force in nature, it too can contribute to the Higgs particle mass, just as the weak nuclear force does, and pull the Higgs mass up.
  • If there are extra Higgs particles (beyond the minimal five) they too can cause effects (partly through new forms of mixing among the Higgs fields) that move the Higgs particle’s mass upward.

Alternatively, one also might conclude that a limited form of the hierarchy problem is still a lot better than the original one, and maybe nature is happy with that. It has always been quite easy for theorists to find theories with mildly-split supersymmetry — in which the superpartners of the matter particles (the quarks, charged leptons and neutrinos) are roughly 30 – 100 times heavier than the superpartners of the force particles (the gluons, the photon,  the W and Z particles) and of the Higgs itself.  Historically such theories were usually discarded by theorists as unpleasant, because they don’t entirely solve the hierarchy problem; one would expect the Higgs field’s value either to be zero or to be roughly as large as the squark masses. But the justification for that bias, though reasonable, was unfortunately always a bit thin.  More and more theorists around me seem to be retreating from their view that the hierarchy problem needs a complete solution, and considering the possibility that while the superpartners of force particles and of the Higgs might be accessible at the TeV energy scale, the masses of the superpartners of the matter particles may lie perhaps 100 times higher, out of reach of the LHC.

Figuring all of this out will require, among other things, high precision measurements of the Higgs particle, assuming the current hints are confirmed in 2012. We will need to compare its properties to what is expected in the Standard Model for its production rates and its decay rates, to see if there are any deviations from the Standard Model, and also look for any exotic decay modes, which it may well have. The Higgs particle is a sensitive creature, as I’ve emphasized, and it (or they, if there is more than one) will potentially give us many insights into the physics that may lie just beyond our current reach.

Some Final Comments

You might well ask whether we should start the process of walking away from supersymmetry already, since there’s nothing in the data that directly supports its presence.  Well, I still think this is a bit early, just because I think the search strategies still have some holes in them, though these are clearly somewhat smaller and harder to identify than they were this past summer.  But a more interesting reason to keep looking for supersymmetry was articulated to me early on in 2012 by one of our most clear-headed theorists, Nima Arkani-Hamed.  If I remember it right, he put it this way: while the Higgs (if it is really there at 125 GeV/c) is a tiny bit too heavy to be part of a typical variant of supersymmetry, it is just a tiny bit too heavy.  Within the Standard Model, the Higgs particle’s mass has nothing much to do with the W and Z particle masses; it is determined by a separate set of considerations, and could easily have been 10 GeV/c or 500 GeV/c.  In most extra dimensions models, composite Higgs models, technicolor models, and the like, there is also no reason for the Higgs mass to be particularly close to the W and Z masses, and in some cases there’s no Standard Model-like Higgs at all!  The only well-known class of models that rather generically predicts a Standard Model-like Higgs not too far from the Z particle mass is supersymmetry.  [But see Spencer Chang’s comment below; he disagrees.] And mildly-split supersymmetry (which I described above) pulls the Higgs mass up into the desired range.

This is not a proof of anything, but it maintains the suspicion among many theorists that some unusual variant of supersymmetry might lie around the corner in LHC data.  Of course, maybe it’s just a coincidence, or maybe we’ve entirely overlooked some other compelling mechanism which could make these masses naturally similar.  Well… for now there’s nothing to do but gather more data, confirm the Higgs particle is really there at 125 GeV/c2, measure it carefully, and keep thinking.

What do I personally think about all of this? I don’t know what to think, and I haven’t for a decade or so. I think there are too many possibilities, and that theorists lost their guiding principles back around 1998, when dark energy was discovered (posing an even more thorny hierarchy problem) and then the possibility of large extra dimensions was pointed out (indicating to me that we theorists can fail for decades to recognize interesting experimentally-allowed possibilities.) Which is why my focus, personally, is on making sure we get every ounce of information out of LHC data. Sure, we’d better look for these variants of supersymmetry that I’ve mentioned. The motivation for them is clear enough right now. But notice the motivation has shifted from last year, because of the new knowledge we have from the 2011 data. We’d be wise to consider that what nature really has in store for us may not seem theoretically motivated until 2013, or 2015, or 2020, after a lot more LHC data… and so I think we should approach the 2012 data in a very open-minded fashion.

46 Responses

  1. Aw, this was an incredibly good post. Finding thee
    time and actual effort to mwke a very good article… butt what can I say… I procrastinate a lot and
    don’t manage to get anythiung done.

  2. Ok, but frankly I’d prefer an interesting world to a boring one. Perhaps “interesting” is my definition of beauty. Is Quantum Mechanics beautiful or ugly? Well, it’s extremely beautiful, probably in ways we haven’t begun to understand yet. One measure of this is that its very meaning is still unclear even 90 years after its original formulation, during which time it’s held the endless fascination of countless extremely smart people. If Laplace had been right, and the world had been classical, non-relativistic, and predictable, then I don’t think physics would have been a particularly interesting field. Would you really have gone into it?

    Respectfully, since you express a strong desire to see something beyond the SM, it seems you actually *do* have an aesthetic preference. I’d suggest that for you too the correct definition of beauty is “that which is interesting”, or “that which continues to puzzle me”. Can I make that precise? Nope. But surely you’d be just a little disappointed if the next 50 years turned up nothing but the annual discovery of some tedious Z’ extensions to the SM. Sure, we’d be discovering how nature really is, but after a while it would make accountancy seem thrilling.

    1. Your comments are always sharp, but this one is also very slippery. Before you were talking about “beauty”. Now you’re talking about “interesting”. The first is an aesthetic criterion, the second an intellectual one. I would not elide these two things together.

      I think your question about Laplace is entirely unfair. You pose a straw man — “what if nothing had been learned about the fundamental laws of nature for the last 200 years, would you have wanted to study physics?” The answer to your question does not exist, because the question is ill-posed; if you imagine that Laplace were right and nothing else had been learned since then, nobody would be working in the field; but if Laplace were right AND enormously exciting things were still being found out about this non-relativistic, predictable world — say, about the nature of strong gravity and the structure of matter — then sure, of course I would have considered going into it, though who could possibly say I would have actually chosen it? That depends on so many things…

      Again, I think you are making a big mistake confusing an “aesthetic” preference for an “intellectual” one. I disagree that “beauty” is “that which is interesting” or “that which continues to puzzle me”. I go to concerts not because music interests me but because it moves me emotionally; music which is only interesting (and some of contemporary music is in that category) I only want to hear once. Music that is beautiful I carry with me for a lifetime. The same is true for painting, dance, poetry, and other cultural experiences that I enjoy. Landscapes, also; do I really love the view of Mount Rainier because I find it interesting, or because it puzzles me?

      So I, at least (perhaps you do not) have very different experiences in the presence of things that I find interesting from those that I have in the presence of things that I find beautiful, which forces me to reject your viewpoint out of hand. Even in science, this is true; interesting equations and beautiful equations go in different categories, which of course can overlap but do not do so entirely.

      What I do seek, in physics, is understanding, with the usual caveats that this is not something one attains through physics equations; at best one really attains predictive power. That is absolutely not the same as seeking beauty; the most beautiful things in life are ones that I am sure I do not understand, and cannot predict.

      Finally, your statement about Z’ accountancy is also wrong, I think. Consider what happened when chemistry found one element after another, or when the search for particles in the 50s found so many hadrons. Accountancy is often the predecessor to a deep insight; it would be very exciting as we searched for that insight, and I doubt many particle physicists would give up hope. Perhaps I might not live to see this understanding achieved, but that would be something I could not know in advance.

      One general point: We can continue to talk about these issues, but I would prefer you not try to guess how I think and feel. You’re obviously very smart and have interesting things to say, but guessing my state of mind is not your strong suit.

      1. I’m actually not very interested in the central argument here (I am interested in the eventual resolution, just not the exhaustingly obstinate—and probably critically important—reality-TV-grade back-and-forth that I can’t seem…to stop…stop reading…can’t stop reading), but I’m fascinated by the tangential debate around ‘interest’ and ‘beauty’. For whatever my random opinion is worth here, while I agree with Professor Strassler’s general point about presuming to know another’s mind, I think it bad form to insist two things so intimately coupled within the clammy volume of our skulls are distinct and unrelated. In Crofton’s defense, she may be alluding to the possible unification of such apparently disparate characteristics as ‘interesting’ and ‘beautiful’ suggested by Jürgen Schmidhuber and others (http://bit.ly/N9aPHF). As in physics, recognition that two things (the electromagnetic and weak forces, say, or, in this case, aesthetics and rationality/emotion and intellect) are simply aspects of something more fundamental—if true—is highly desirable and profoundly useful in removing the clutter of misconceptions and false assumptions impeding progress.

        But I’m just a random passerby—and an artist to boot—what do I know from physics?

        I probably won’t trouble you again.

        P.S. No disrespect intended. Also, I claim disinterest while being forced to admit some insipid neural subsystem enjoys it all quite a bit 🙂

  3. Hi there. I have a question: Are you (and more generally the average theorists gathered around the water cooler) *hoping* SUSY shows up or not? The idea of SUSY might indeed be extremely beautiful, and perhaps everybody wishes the universe had pure unbroken SUSY. But it doesn’t. From what I’ve heard on Science Friday and read here, to match the standard model it needs to be broken with multiple arbitrary parameters, thus becoming very ugly. So would you rather that this ugly version is found to be true, or would you rather that no SUSY is discovered, letting us hold out the hope for another resolution of the hierarchy problem but leaving those swarms of additional terms out of the SM? (If you had the choice 😉 )

    1. Well, I personally am not hoping anything in particular, except that the Large Hadron Collider gives us information about the many puzzles that remain concerning the known particles and forces (i.e. the Standard Model of particle physics). Anything beyond the Standard Model would be fine with me. I’m interested in reality, not mathematics — I want to know what nature is up to, and I don’t care if nature’s equations are ugly from somebody’s personal aesthetic viewpoint. Is quantum mechanics beautiful or ugly? Is the Standard Model beautiful or ugly? You can make arguments either way, and in my view constructing such arguments, and trying to quantify what is more or less beautiful, is pointless. Science is about figuring out how nature works, not judging its aesthetic qualities; consensus on whether a theory is valid comes from successful prediction, not from winning a beauty contest.

      It’s very dangerous, in my view, to put elegance criteria onto physics. It’s only one of several possible criteria for selecting good research directions, and I can give you a lot of cases where it led people astray. I think that a lot of what we call `beautiful’ today is actually what is `true’, viewed as beautiful only after the fact by scientists who want to believe the world is beautiful. Look at the way string theorists pivoted from saying that “string theory is beautiful because it is unique, despite its inability to make a definite prediction” to saying “string theory is beautiful because it predicts a huge landscape of possible universes” (which is not a fact unique to string theory); the aesthetic move was a bit breathtaking.

  4. Theory with weak postulates has epicycles, then a rewrite. Mechanical Newton fell to Maxwell and EM. Physics observes mirror-symmetric vacuum toward massless boson photons. Fermionic mass requires symmetry breakings. Physics has a white-painted black swan.

    Visit Australia (two geometric parity Eotvos experiments). A vacuum left foot causes dropped opposite shoes’ trajectory divergence. Geometric chirality emerges at four non-collinear, non-coplanar atoms inside crystallography’s enantiomorphic space groups. Such periodic single crystals are in-phase self-similar at all larger scales. Theory is empirically sterile. Look at a black swan.

  5. (I get your point about what you said in the beginning. I hadn’t read the comments yet. I just meant the sentence where “supersymmetry as an idea” was having “all its possible variants” ruled out…)

    No matter if we interpret the grammar differently. But differences in physical interpretation are potentially much more interesting.

    The way I have understood the line of stringy phenomenology research pursued by Gordon Kane et. al., which is what I was referring to, the most important implications come from very mundane observations, like the fact that the lightest moduli naturally wants to be within an O(1) factor of the gravitino mass, which sets the SUSY breaking scale, because the mechanisms are related. Also, this work is focused on characterizing what is _likely_ to be the case, not certainties. Sometimes the level of skepticism I encounter regarding this makes me think the person has over-interpreted the claims here. ( http://arxiv.org/abs/1112.1059 , its refs, and others by Kane in the arxiv if you want to look)

    I’m of course not able to personally vouch for all the logic and numerical detail right now (though I’d like to check as much as I can myself, eventually) but it just seems to me that these arguments are pretty simple and I don’t see any particular spot where there is any “hocus pocus” hiding nor extreme difficulty.

    Kane predicted a Higgs mass of “about 127 GeV” back in August 2011, which may be a coincidence, or it may be indicative of him being on to something. Im personally thinking compactified string theory has a lot of reasons to be assessed good and increasing odds of being realized. I understand there are subjective judgements involved, but who can resist assessing and predicting?

    1. The level of garbage and propaganda surrounding the Higgs is getting pretty ridiculous.

      You realize, yes, that by August 2011 the window for the Standard Model Higgs was down to 115 to 140 GeV, right? So your chances of getting within 5 GeV of the right answer is 15%. Many theories before Mr. Kane predicted a range that included 125 also. I’m completely unimpressed both by the science and the propaganda. Most of my friends who are experts in compactification (which Kane is not — he relies on one of his collaborators — and I am not an expert either) are not convinced of the assumptions on which they base their arguments. It all sounds good. But is it really? I’ve heard lots of arguments that sounded good over the years… and most of them are now known to be wrong. None of them are known to be right.

      Do not judge science on the ability of the scientist (who wants his or her Nobel prize and is trying his or her best to convince you) to present a compelling argument. A great salesperson can create a terrific argument; a great physicist does not need one.

      1. I was paying attention to the excluded ranges through this period, yes. According to the best assessment of the two LHC experiments, it is correct to within 1 or 3 GeV. And the research was clearly only trying to predict it within a comparable margin anyway.

        There are indeed plenty of models that have been built, predicting one thing or another, but this is the only line of research I know of that was attempting to characterize a generic compactification scenario. Am I wrong? This a really important distinction that raises the importance of the prediction by many orders of magnitude, because there is no big menu of similarly generic predictions that Im aware of. Just random constructions.

        All of the cautions sound, of course, wise and appropriate in general. But Im not asking to give Kane a Nobel prize. I just think the (apparent, preliminary) correctness of his prediction warrants looking at his construction more closely. If your theorist friends have well-founded doubts, I definitely would love to read about them. If not a paper, I wish they would write a blog entry or something. I cant think of anything more relevant to examine in high energy phenomenology right now than the theory that a) is generic, or largely so, and b) predicted the Higgs mass to within about 2 GeV.

        I can understand the “interpret all uncertainties as pessimistically as possible” mindset if we were going to claim some discovery, but thats not what Im doing. Im simply trying to assess the relevance of this construction according to the best available information. The generic cautions don’t offer me any logical reason to not be interested. Believe me, I want to know if there are good reasons.

    2. Hi Cliff,

      there`s no point in coming here to argue with Prof. Strassler.
      You better study carefully the truth and wisdom that is written in the “bible” and you`ll probably find more peace and satisfaction … You know what I mean 😉

  6. It is amusing that in a technicolor model the topless technipions should be very like as the sleptons except for lepton number, and the topless tecni-diquarks be like as the squarks but for the baryon number. At least in particle content, technicolor is almost the same that a SUSY that violates B-L, the difference being in the lack of gauginos here. So perhaps we should not make a big thing of the lack of squarks, and concentrate on catching gluinos, winos and similar beasties.

    1. That’s true of some technicolor models; but you can also have bound states that mimic gluinos and winos too. I think clearly it is the Higgs that is the defining issue for technicolor.

      Look, if we find *anything* beyond the Standard Model predictions, it will take us years to be sure we know what it is. There will be a lot of (healthy) debate and many additional measurements will be needed to be sure.

  7. Im glad to read what your assessment is on this. However, I just take issue with how you say ruling out “all possible variants” might take a decade. Obviously SUSY cant ever be ruled out if its broken at high enough energy. Im sure Im not telling you anything you don’t know, but then why this statement?

    I think a better way to summarize it would be “It will take a long time, perhaps a decade, to rule out all the variants of supersymmetry that can satisfactorily resolve the hierarchy problem. However since this depends on a not-sharply-defined choice of what constitutes an ‘unnaturally small parameter’, this exclusion will also be subject to some provisos.”

    I understand the reasoning for glossing over this subtlety in such explanations, but I think it might become important because compactified string theory predicts that SUSY is broken higher than naturalness arguments alone would prefer. Obviously models that descend from a consistent higher energy picture are the ones that are most motivated and, ultimately, most likely to appear.

    1. I tried to be precise in the core of the article. For instance, at the beginning I said, “Is supersymmetry, as a symmetry that might explain some of the puzzling aspects of particle physics at the energy scales accessible to the Large Hadron Collider [LHC], ruled out yet?”

      You are responding I think to a comment reply where I was a little more careless. But obviously I don’t disagree with you, and I hope and think I was clear enough in the main part of the article.

      As for what string theory predicts, I am very far from convinced that people understand what they are doing in these string constructions. I don’t agree with your last paragraph at all. Not that it matters whether we agree or not.

      1. Thanks for this further clarification.

        To me it was not quite clear before if you think that the idea of supersymmetry as a whole (and everyhing that depends on it that is probably bogus anyway as I red from this answer ?) should be given up, if (hypothetically) all the holes are closed in few decades without anything showing up …

        Nice article 🙂

  8. I have always wondered why the W and Z cannot be considered superpartners to the leptons. Why can’t do the superpartners half to be a half integer less? Also, is there any models of the Higgs being composed of gluinos or squarks?

    1. The W and Z have many properties that make it impossible for them to be partners of any of the leptons and neutrinos. As a very simple example: the W and Z interact directly with quarks, while leptons do not. Also, the W and Z particles interact rather strongly with the Higgs particle (which is why they are relatively heavy) while the leptons and neutrinos do not (which is why they are lighter). Most of the other properties in question are slightly more involved to explain, but are just as convincing.

      No, there are no models with the Higgs being made from squarks or gluinos. It would be very difficult to make such a Higgs field interact properly with the matter fields to ensure the masses of the quarks and leptons come out as observed.

  9. Matt, I would argue that a light Higgs just above the Z mass is a bit more generic than SUSY. With just the Standard Model, vacuum stability sets a mass that is near 125 GeV. Gauge-Higgs unification also ties the Higgs mass to be close to the Z. Finally, if you are in a composite Higgs scenario where you radiatively generate the Higgs quartic, you might argue that the Higgs mass starts low and that the radiatve corrections get you to 125 GeV due to the masses of the top partners.

    1. Thanks, Spencer. I remember Nima claims the composite Higgs mass comes out too low if you radiatively generate the quartic. As for gauge-higgs unification, what’s your favorite model there?

      Oh, and on the Standard Model, why should the Higgs be sitting at the edge of vacuum stability? (If this is even the case, once you account for dark matter and neutrino masses…)

      1. In the minimal composite Higgs paper with Kaustubh, Roberto and Alex, they get some points with m_H ~ 125 GeV, with their rho at about 4 TeV, so it is possible. No favorite models of gauge-HIggs unification, but at the very least, one of the model independent predictions of that scenario is that the quartic is set by gauge coupling.

        I thought you could make a “living dangerously” prediction of the Higgs mass, that it shouldn’t be too far above the stability bound. For instance, Nima’s no eternal inflation paper wants the Higgs mass to be light, although his bound is < 110 GeV.

  10. “Pizza is a great idea too, but there are a million ways to make one, so you can’t conclude that nobody makes pizza in town just because you can’t smell tomatoes”

    Pizza w/out tomatoes!! that’s like saying we discovered half SUSY spectrum already 😉

  11. On the hierarchy problem.

    I seem to remember learning that the ratio of the strength of the electric force to the gravitation force was similar to the ratio of the classical radius of the electron to the size of the visible universe.

    Is this fact ( and I may have this totally wrong ), still considered significant in anyway ?

    1. Size of visible universe: 10^10 years * 3*10^7 seconds/year * 3*10^8 meters/second = 10^26 meters
      Classical radius of electron: 2 * 10^(-15) meters

      so the ratio is 10^41.

      The ratio of the strength of gravity depends on how you measure it, because, of course, gravity depends on mass (actually on energy, but for stationary particles E = mc^2.) For the forces between two electrons, the strength of gravity is the square of the electron mass to the Planck mass

      (0.0005 GeV/10^19 GeV)^2 = 10^(-44)

      while the strength of electromagnetism is about 1/100, and thus the ratio of the strengths of the two is about 10^(42). There are some ambiguities of factors of 2 here so getting to within an order of magnitude means they’re basically the same.

      So that looks interesting. BUT: this is a coincidence.

      If you did this for a neutrino or a proton or a muon or a Higgs particle you’d not find this coincidence, because the classical radius of a particle goes like the inverse of its mass while the strength of gravity goes like the mass-squared. It’s just an accident that it works for the electron; it doesn’t work for any other particle.

  12. Good article… but if there really is no Higgs below, say, 500 GeV, what then happens to SUSY?

    I always break out laughing at the thought of both left handed and right handed *scalars*. Then the thought of the non-top squarks nearly degenerate in mass makes me nearly giddy with the ridiculousness of it all. But hey… if it is right, the ridiculousness will be the unique signature.

    1. a) if there is no Higgs below 250 GeV or so, SUSY at the 1 TeV scale would probably be excluded. There probably is a loophole but very narrow. Most variants of SUSY would be long gone if there is no Higgs below 150 GeV.

      But remember, because Higgs particles are so sensitive and can easily be quite different from expectations, it will be many years before we know there is no Higgs below 250 GeV. http://profmattstrassler.com/2011/12/04/why-10-years-to-be-sure-theres-no-higgs-particles/ .

      b) there is no such thing as left- and right-handed scalars. There are, however, separate scalar partners for the left-handed top quark and for the right-handed top quark (whose field also produces the left-handed top anti-quark — so if you prefer you can say there is a top squark and a separate anti-top squark and skip the handedness language.)

      1. Well, b) is semantics, actually, except… what is the total number of, say, charge +2/3 scalar states with 1 unit of top quantum number in SUSY… is it… 1 or 2? Same for -2/3 -1 top scalar states, 1, or 2? Totallying to… 2, or 4?

        1. Semantics, yes. The physics is that there is one Dirac fermion (the top quark) with charge +2/3, built from two Weyl fermions, and there are two scalars with charge 2/3, one for each Weyl fermion. The fermion and the two scalars will have different masses since supersymmetry is broken, so there are three separate particles with three separate masses to find.

          Same is true for every other quark.

      2. well, might be true, if the SUSY conjecture is correct. I still break out laughing! That there are a pair of scalars (possibly with different mass) descended from a single fermion with one mass… ha! Hardly seems like a simplification, more like a trope. Someday if neutrinos are proven to be Weyl (vile?) and not Dirac (to rock?) that will bolster the picture. Maybe it is right! That would be great, and would show that particle physics turns toward the complex, but only a little bit.

        1. Well, if you play with the mathematics, you see why this is a very natural consequence of geometry to have things organized in this way. Of course the question of whether it is true or not of nature is a question for experiment, not theory.

      3. Sure, but `natural’ is in the eye of the beholder. Dirac fermions aren’t natural at all by most current theoretical eyes, I guess. On a slightly different topic… that the u,d,s,c,b quarks all have scalar partners that are nearly degenerate in mass… wow, what a possibility. But it is the sort of unusual and (to experimentalists) un-natural prediction that would validate the whole SUSY industry if it turns out to be true.

  13. Very nice article. The part about only Susy predicting a Higgs mass close to the W and Z was new to me.

    “I hope that in late 2012 or early 2013 we’ll start seeing the remaining gaps start to close, but I suspect it will be more like late 2013 or early 2014 before this happens. [Don’t worry, I’ll let you know.]”

    Are you forgetting the break for the 14 TeV upgrade?

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A decay of a Higgs boson, as reconstructed by the CMS experiment at the LHC