Matt Strassler [January 28, 2013]
Supersymmetry is certainly a great idea — it is the one symmetry of space-time that is consistent with the other symmetries of space-time but hasn’t been discovered in nature. But is supersymmetry part of the real world? If it is, it must be hidden (often said to be“broken” [and ``spontaneously'' so] — see Figure 2 of this article). Why is that?
All particles are either fermions or bosons. A consequence of supersymmetry is that there are superpartner particles for all known particles; the superpartner of a fermion is a boson and vice versa. Were supersymmetry unbroken, the up quark and its superpartner, the up “squark,” would have to have the same mass, so we would have found the up squark long ago. So supersymmetry, if it is true, is hidden; but the superpartners are still out there, just with larger masses. We have to try to produce them at the LHC, and then look for indirect signs of them following their decay, much as we look for the Higgs particle by looking for its decay products.
One reason supersymmetry is popular is that it apparently makes Einstein’s old puzzle, of how to combine gravity with the other forces into a consistent whole, somewhat easier to solve. But if that were all it did, superpartner particles could have masses at the scale where quantum gravity becomes relevant — as much as 1015 (a thousand million million) times too heavy for them to be discovered at the LHC. But if the superpartners have masses around 1 TeV/c2 or below, making at least some of them accessible at the LHC (and let’s call this LHC-accessible supersymmetry), then supersymmetry might resolve one of the other huge problems in particle physics. This is the hierarchy (or “naturalness”) problem.
In the Standard Model, the fact that the Higgs field’s value (246 GeV), and consequently the masses of the W and Z particles (80.4 and 91.2 GeV/c2), are so much smaller than the mass scale associated with quantum gravity — by a thousand million million (1015) — appears to be an extreme accident. If you write the Standard Model (the equations that describe the known elementary particles and forces), and you change any of its details by a tiny, tiny amount, you will find that the Higgs field’s value (and the W and Z particle masses) will change drastically, either becoming (a) zero or (b) much, much larger — typically 1015 times larger. Getting the Higgs field to be 246 GeV seems extremely unnatural — it seems a little like balancing a pencil upright on a ball which is balanced on the nose of a seal which is balanced on the top of an iceberg. How does nature do this???
Well, if all the superpartner particles have mass near to 1 TeV/c² = 1000 GeV/c² or below, then it turns out that the math of supersymmetry works to get this balance automatically! Basically the shift in the Higgs field’s value caused by any particular boson is nearly canceled by its superpartner fermion, and vice versa, as long as particle and partner have masses that aren’t too different.
So “LHC-accessible supersymmetry” might solve the hierarchy problem [i.e. the naturalness problem] and if it does, it predicts many or all of the superpartner particles should have masses near 1 TeV/c², putting them within reach of the LHC experiments. The challenge is that there are innumerable ways to hide [i.e. break] supersymmetry, each one of which gives a variant of supersymmetry with different details for the superpartner particles’ masses and decay patterns… and this makes it hard (painstaking, but not impossible) to completely rule out the idea of LHC-accessible hierarchy-problem-resolving supersymmetry. One has to systematically rule out all of the possible variants, and that’s hard work.
One remark before we continue: it is important to distinguish supersymmetry in its most general form from “minimal supersymmetry”, in which the only particles accessible at the LHC are those we already know (except with five types of Higgs particles), plus their superpartners.
So far, the LHC experimenters have three strong pieces of information about supersymmetry, all negative, but none of them definitive. They are the following (pay special attention to the third):
- As yet, LHC data shows no signs of superpartner particles, ruling out large classes of supersymmetry variants. We can’t draw any sweeping conclusions yet, because plenty of other variants would not yet have been seen.
- A measurement by the LHCb experiment is within 30% of what is predicted in the Standard Model. Many variants of supersymmetry predict a larger value, and are therefore ruled out.
- In minimal supersymmetry, it is very difficult to solve the hierarchy problem and have a Higgs that resembles the simplest type of Higgs (a “Standard Model Higgs”) and is heavier than 120 GeV/c2. Data reveals a very Standard Model-like Higgs with a mass of about 125 GeV/c2. So it appears minimal supersymmetry that solves the hierarchy problem easily is nearly excluded.
The reason why supersymmetry forces the Higgs particle’s to be lightweight comes from the fact that (a) the mass is partially set by the strength of the Higgs interaction with itself, and (b) that strength is related, in minimal supersymmetry, to the strengths of the weak nuclear and electromagnetic forces, which we already have measured. (No such relation between these quantities holds true in the Standard Model itself.) If it weren’t for the fact that the top quark has a large mass, the lightest Higgs particle would actually have to be lighter than the Z particle, 91.2 GeV/c2. Effects from top quark “virtual particles” can pull the lightest Higgs particle’s mass up to 120, but not all the way to 125, unless some nasty adjustments are made to the theory, or one considers non-minimal supersymmetry.
John Ellis in his Higgs Symposium talk specifically discussed the impact of these measurements on a subclass of variants of Minimal Supersymmetry (the “Constrained Minimal Supersymmetric Standard Model”). I’ll let the experts read the talk and spare non-experts the details. Overall, my read is that only a small fraction of the variants of this subclass of models is still consistent with data.
But non-minimal variants of supersymmetry may have extra particles and forces that can shift the Higgs particle’s mass up to 125 GeV/c2. As Nima Arkani-Hamed described in his Higgs Symposium talk, the simplest non-minimal models that could do the job would have
- Extra spin-0 Higgs-like fields (and their superpartners), and/or
- Extra spin-1 Z-like fields (and their superpartners).
These extra “singlets”, as they are called, are not affected by the electromagnetic or by the strong or weak nuclear forces, but can interact with the Higgs fields and shift the mass of the lightest Higgs particle in the theory up to the 125 GeV/c2 observed in data. These singlets have experimentally observable consequences that can be sought at the LHC.
While the experimenters are looking for signs of singlets, standard searches for the superpartners of the known particles continue. There is special focus right now on those superpartners which must be LHC-accessible if supersymmetry solves the hierarchy problem — the ones that interact most strongly with the Higgs fields. These are the superpartners of the top quark (and bottom quark), the Higgs particles, the W and Z particles, and even the gluon (which interacts with the Higgs fields indirectly but sufficiently strongly to be important.)
A rather different possibility, which has been around for a long time and which Arkani-Hamed likes (and I used to not be very fond of, but the Higgs mass measurement forces me to pay it more attention), is that supersymmetry does not entirely solve the hierarchy problem, but solves it part-way, with the remainder explained by a lucky accident or though a selection bias (such as the “anthropic” or “structure” principle, whereby the reason our part of the universe looks unusual is that (a) the universe is much more immense and diverse than we realize, (b) most regions are uninhabitable, and (c) only in rare regions with very unusual properties can there be anything like stars, planets, and evolution.) This is the notion of “split supersymmetry”, whereby the fermion superpartners of the photon and the W, Z and Higgs particles remain relatively light and LHC-accessible, while the boson superpartners of the matter fermions are heavier by about a factor of 100 or more. (This kind of splitting arises very easily in theories of supersymmetry breaking, and in fact one typically has to work to avoid it.) A complete solution to the hierarchy problem is abandoned, but it turns out this idea has some nice features too, which I’ll skip (but see Figure 1).
For our purposes, the key point is that this type of splitting of the superpartner particle masses can easily lift the Higgs particle’s mass to 125 GeV/c2. And as Arkani-Hamed pointed out, the absence of LHC-accessible boson superpartners will cause the fermion superpartners to have rather long lifetimes, long enough that they may travel a macroscopic distance (millimeters to meters) before they decay. That means they would be discovered in searches for relatively long-lived particles that decay while traversing a detector like ATLAS, CMS or LHCb. Not enough searches of this type have been done yet on the 2011-2012 data, so even without new data, there are opportunities for discoveries over the coming two years, as the already collected data is further analyzed.
Arkani-Hamed’s current view is that if supersymmetry exists and is LHC-accessible, then the key question is whether supersymmetry is natural though non-minimal, or minimal though not natural (Figure 2). This will most likely be resolved (if supersymmetry exists and is LHC-accessible at all) during the 2015-2020 period, though progress might certainly occur sooner.