The Large Hadron Collider at CERN in Geneva is now up and running but instead of being delighted, many theoretical physicists are beginning to get worried. They see the fruits of their long and illustrious careers potentially turning to ashes. The reason? The LHC hasn’t found SUSY.  Alessandro Strumia, a theorist at the University of Pisa in Italy was quoted as saying “Privately, a lot of people think that the situation is not good for SUSY. This is a big political issue in our field. For some great physicists, it is the difference between getting a Nobel prize and admitting they spent their lives on the wrong track.”

What is SUSY?

Most famously, the LHC was going to find and pin down the Higgs boson, the hypothesised quantum of the Higgs field which endows ordinary matter-particles with their mass. You may also recall the famous lawsuit which tried to shut the Collider down on the grounds it would make dangerous quantum black holes (no sign yet, and anyway, they’re not dangerous). Then there was excitement at the possibility that large extra dimensions might be found, the first experimental support for String Theory. And then … there was the expected confirmation of SUSY (short for supersymmetry), which to non-physicists unfortunately meant precisely nothing.

The Standard Model of particle physics describes all the fundamental particles known to exist plus the predicted Higgs boson mentioned above. There are matter particles (called fermions) like quarks, electrons and neutrinos; and force-carrying particles (called bosons) such as gluons carrying the strong force, photons the electromagnetic force, and the Z and W bosons mediating the weak force. In the Standard Model, matter-fermions and force-bosons are fundamentally different kinds of creature distinguished by their spin. Fermions have half-integer spins, typically 1/2 for fundamental particles; bosons have integer spins with typical value 1 (the Higgs is the exception with spin 0).

Back in the early 1970s, deep in the Cold War, a bunch of soviet physicists began to consider a possible symmetry of nature in which every fermion might have a corresponding boson superpartner, and every boson a corresponding fermion superpartner. So for instance, the electron – a fermion – might be partnered with a new boson superpartner, the selectron; the photon – a boson – might have a fermion superpartner, the photino. The Soviet version of supersymmetry was initially just another theoreticians’ fancy and was ignored in the West, particularly as the papers were in Russian. However, by the early 1980s US physicists such as Howard Georgi (Harvard) and Savas Dimopoulos (Stanford) had managed to get the theory to the point where it made contact with the mathematics of the Standard Model.

Thus was born the MSSM, the Minimal Supersymmetric Standard Model. The superpartner of each particle in the Standard Model was meant to have exactly the same properties as the particle itself, except that its spin would be different by 1/2 (recall that the difference between fermions and bosons is their spin). However, at first sight this could not possibly be the case  or we would have seen all these new sparticles (sic) by now. For supersymmetry to be a real symmetry of our universe, the superpartners would have had to have been hidden up to now, by having a lot more mass than their Standard Model counterparts. When this happens, we call the symmetry broken. If supersymmetry was broken, this could allow the supersymmetric partners to be hiding at energies just higher than could be seen with the previous biggest collider, the Tevatron.  With the LHC now on-line, the hunt was on for evidence of superpartners to confirm that SUSY was real.

So why is SUSY important?

SUSY is important for four main reasons.

1. The ‘Hierarchy’ Problem.

The Standard Model relies on the Higgs field and its quantum, the Higgs boson to give matter-particles (and the W & Z bosons of the weak force) their mass. However, the particles of the Standard Model also return the favour, giving mass to the Higgs. In particle physics, mass is measured in terms of energy (E = mc2). For example, the mass-energy of a proton is just under 1 GeV (Giga electron Volts). The heaviest observed elementary particle is the top quark at 172 GeV (note that it weighs more than 172 protons!) while the tiny electron is just 0.5% of a GeV. There is good evidence that the mass of the Higgs particle is between 115 and 185 GeV and it’s probably less than 144 GeV. Note: the reason that the Higgs is hard to find despite all the LHC’s power is that its production rate is less than one in a billion collisions. The new Higgs then promptly decays in 10-25 seconds to particles which are themselves hard to separate from the background left by more common sorts of collision.

So now we come to the problem: when the calculations are done, each kind of known particle with mass should independently contribute of the order of 1,000,000,000,000,000 (1015) GeV to the mass of the Higgs boson! This can’t possibly be right – somehow there has to be some kind of cancelling out. As fermions contribute to mass with one sign, and bosons contribute with the opposite sign, SUSY is just what’s needed. In SUSY each fermion/boson has a boson/fermion superpartner and the contributions will then cancel. In fact if the particle and superpartner masses were the same, the cancellation would be absolute, which would be no use at all. But we know that’s not the case and that the superpartners need to be heavy. If their masses are in the 1,000 GeV range (i.e. 1 TeV up) this may be enough to put the Higgs mass in the right zone. It’s also the mass range where the LHC would be able to see the superpartners.

2. Grand Unification.

The Standard Model brings together three of the four fundamental forces: electromagnetism, the weak force and the strong force (gravity is excluded) but it does so in a rather kludgy way. Technically the forces emerge through three separate symmetry groups: SU(3), SU(2) and U(1) where the force carriers (the eight strong force gluons, the W+, W and Z0 weak force bosons, and the electromagnetic force photon) each correspond to their respective group generators. It is believed that the kludginess goes away if these forces are really different aspects of the same force, defined via a higher-order symmetry group. But if this is so, then why don’t all the forces have the same strength? It turns out that the differing strengths we see around us is an artefact of our low-energy environment. Turn up the temperature, increase the energy of interacting particles and the strong force gets weaker and the electromagnetic force gets stronger. At an elevated temperature of around 1027 K the forces merge into one, the electronuclear force … except that they don’t, quite. However, if you add in the contributions of the extra particles required by SUSY then mirabile dictu, the three force-strengths coincide. This is called gauge coupling unification and is taken to be further supportive evidence for supersymmetry.

3. Persuasive Dark Matter candidate.

Over the last thirty years evidence has accumulated that most matter in the universe is Dark Matter. Initially Dark Matter was supposed to be comprised of massive objects (MACHOs – Massive Compact Halo Objects) such as burned out stars or dark planets. But microlensing observations have shown there are far too few of these so the smart money is now on WIMPS (Weakly Interacting Massive Particles). It’s not easy being a Dark Matter particle though. Dark Matter particles can’t easily interact with atoms and molecules, or with electromagnetic radiation or we would have already detected them. They must be moving rather slowly too, so that they can be gravitationally-bound around galaxies: that rules out light particles such as neutrinos. Finally, they must be stable since their formation 13 billion years ago in the Big Bang. No particle of the Standard Model fits the bill. However, supersymmetry has an ideal candidate, the lightest supersymmetric particle called the neutralino.

Neutralinos, precisely because they have the attributes of Dark Matter would be extraordinarily difficult (but not impossible) to detect. However, they would be the final decay products of heavier and unstable supersymmetric particles such as squarks and gluinos which should be within the range of the LHC. The neutralino mass is thought to be in the 100-1,000 GeV range – recall the LHC is currently running at 7 TeV = 7,000 GeV, seven times the neutralino mass and will in a few years upgrade to 14 TeV.

4. Essential for String Theory.

String Theory is our current best approach to unifying all the forces of nature: strong, weak, electromagnetic and gravity. However, without supersymmetry the ground state of bosonic strings in the theory are tachyons (a faster than light particle whose squared mass is negative). With the presence of tachyons the quantum vacuum is unstable and rolls down a never-ending potential gradient while radiating tachyon-antitachyon pairs. Supersymmetry stabilises the String Theory vacuum.

How serious is the situation?

Supersymmetry’s role in stabilising the mass of the Higgs particle, which itself stabilises the mass of the Z boson at 91 GeV and W bosons at 80 GeV necessarily implies that the mass of the lightest supersymmetric partner should be in the ‘small number of TeV’ range. The Minimal Supersymmetric Standard Model has 120 free parameters and the LHC is currently searching this parameter space. According to some reports, the LHC has already covered 99% of the low-energy SUSY parameter space and has so far shown up no evidence for supersymmetry whatsoever. There are a lot of physicists right now with an unfamiliar hollow feeling in the pits of their stomachs.

However, it’s still early days in terms of the number of collisions so far analysed, while the LHC is still operating at only half-power. According to noted string theorist Luboš Motl,  the LHC has only probed about 1/16 – 1/256 of the parameter space that is accessible over its lifetime, so higher-energy SUSY has by no means been excluded (although as mentioned, SUSY’s theoretical utility decreases at higher energy ranges).

What if the LHC doesn’t find SUSY?

Let me paraphrase  Luboš Motl’s answer to this very question at the Physics StackExchange.

“There are various alternatives as to how to solve the hierarchy problem – the little Higgs model, the Randall-Sundrum models (which may be disproved at the end of the LHC, too – the LHC is expected to decide about the fate of each solution to the hierarchy problem although there may always remain some uncertainty). But I am convinced that even in the case that SUSY is not observed at the LHC, superpartners with slightly higher masses than those accessible by the LHC will remain the most well-motivated solution.

Dark matter may be composed of ad hoc particles that don’t require any grand theoretical framework – but such alternatives would be justified by nothing else than the simple and single job that they should play. Of course there are many alternatives in the literature but none of them seem to be as justified by other evidence as the neutralino is by SUSY. I think that ‘no SUSY at the LHC’ will by no means “completely disprove” SUSY-particles as the source of dark matter, because this role may work up to 10 TeV masses or so, and much of this higher interval will remain inaccessible to the LHC.

Clearly, if no SUSY were seen until 2012 or 2015 or 2020, the critics of string theory would be louder than ever before. Within string theory, the anthropic voices and attempts to find a sensible vacuum with SUSY symmetry breaking at a high-energy scale would strengthen. But nothing would really change qualitatively. The LHC is great but it is just moving the energy frontier of the Tevatron at most by 1-1.5 order(s) of magnitude or so.

In summary, while it is clear that the absence of SUSY at the LHC would weaken the case for SUSY and all related directions, I am convinced that unless some spectacular new alternatives or spectacular new proofs of other theories are found in the future, SUSY will still remain the single most serious direction in phenomenology. In formal theory, its key role is pretty much guaranteed to remain paramount, regardless of the results of LHC or any conceivably doable experiments. The more formal portions of high-energy theory a theorist studies, obviously, the less dependent his or her work is on the LHC findings.”

That’s the view from the die-hard string theory camp. But many other physicists will just give up on supersymmetry and will hope to God that at least some new physics comes out of the LHC, enough at least to catalyze some new theoretical insights.

What will happen if SUSY is found?

The theoreticians will breathe a huge sigh of relief and immediately get down to calculating the consequences of the new data on superpartner masses and interaction modes. It would shift the discussion to a new question: how and why is supersymmetry a broken symmetry (e.g. why are the masses of the superpartners different from their Standard Model partners)? And we would have found the leading candidate for Dark Matter. It would also be a tremendous boost for string theory itself, which probably needs it.

For further optimistic discussion along these lines see this question at the Physics StackExchange.

Further Reading

 Nature’s Blueprint – supersymmetry and the search for a unified theory of matter and force, Dan Hooper, Smithsonian, 2008.