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:
- Direct searches for the superpartner particles of up quarks, down quarks and gluons have so far turned up nothing, implying that such particles must have masses around, or somewhat heavier than, 1 TeV = 1000 GeV (as long as the lightest neutralino — a superpartner of the photon or Z particle or Higgs particle — is lighter than 200 GeV/c2 or so.)
- The search for the Standard Model Higgs particle (the simplest possible form of the Higgs particle) is suggesting a possible signal of such a particle at a mass of 125 GeV/c2. If this turns out to be true, it has big implications for many supersymmetric models for which such a Higgs mass is somewhat too large.
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.
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.]
But if instead one does make the standard assumptions,
- in any process, the number of superpartners can only change by an even number;
- 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);
- 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.
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/c2 (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/c2 ) 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/c2 or 500 GeV/c2 . 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.