What's so super about Supersymmetry?

The headline discovery out of the LHC was, of course, the Higgs Boson. But the LHC is no one-trick pony. The search is on to find hints of Supersymmetry. What's that, you ask? In this week's column, we'll find out.

All images via NASA/ESA/Hubble.

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This week, we'll talk about some of the fallout following the discovery of the Higgs (the particle, you'll recall, that gives other particles their mass). Physics seems to be in pretty good shape. We've basically confirmed all of the main features of the "Standard Model" of physics. We've now discovered every particle in the model, with no leftovers. But now isn't the time to get complacent. There are still lots of unanswered questions.

You may have heard some murmurs about a popular idea known as Supersymmetry (or "SUSY" to its friends). There's a lot riding on the possibility of SUSY, including a few problems that are — ironically — caused by the discovery of the Higgs itself. So today we're going to figure out:

What's so super about supersymmetry?

The Particle Zoo

This being io9, the particle zoo is probably second nature to most of you, but in case it isn't, let me give you a 10 second backgrounder to get you ready for SUSY.

What's so super about Supersymmetry?

The world of fundamental particles is filled with cool sounding things like quarks and gluons, but at the end of the day, most of the interesting distinctions between particles can be found by putting them very neatly, and quite unambiguously, into two different piles known as Fermions and Bosons. The Fermions are the most familiar particles: electrons, quarks, neutrinos and the like. These are the particles that make up matter. Quarks, for instance, make up protons and neutrons which are, themselves, also Fermions.

Bosons, on the other hand, are the particles of force: photons, the W and Z Bosons, gluons, and the Higgs.

The difference between the two groups comes down to a very weird property — one that I've written about before — known as spin. All known particles have an intrinsic, unchanging spin to them. Except for the Higgs, which doesn't spin at all.

What's so super about Supersymmetry?

Fermions have a spin of 1/2 (one half, that is, of a number known as the "Reduced Planck Constant"), while Bosons have an integer multiple. Since the Higgs has zero spin and zero is an integer, the Higgs gets lumped in with the other Bosons.

Those differences seem like the sort of trivia only the nerdiest physicist could get excited about, but they have enormous consequences. The distinction manifests itself when you switch one particle with another of the exact same type. If you switch two Bosons, then the quantum wavefunction of the universe is multiplied by a +1 (totally unchanged), but if you do the same thing with Fermions, you get a -1.

That's it. That's literally the most important difference between the two, and yet, that -1 is ultimately responsible for something known as the "Pauli Exclusion Principle," which gives rise to everything, from all of chemistry to the behavior of White Dwarves.

What does this have to do with the Higgs?

The Higgs is a pretty important particle in the scheme of things. Did you see the excitement from the Physics community when it was discovered? It's like finding a mint condition Millenium Falcon still in its original packaging.

We were fairly confident that the Higgs would be discovered. It is a linchpin in the Standard Model, something that seemed absolutely essential to explaining why the weak force was so weak.

What's so super about Supersymmetry?

Related to that, the Higgs also explained where the masses of particles come from. That's because the Higgs interacts with just about everything.

But these interactions are a two-way street. Remember Newton's 3rd Law, "Every Action has an equal and opposite Reaction." Since "interaction" is simply a fancy word for "energy" and energy and mass are interchangeable (E=mc^2, remember), the the Higgs doesn't just give mass to other particles, other particles give mass to the Higgs. But here's the weird part. The contributions from other particles can either add extra or subtract from the total. The Higgs mass that we measure at the LHC isn't necessarily the real mass that it would have if we could strip away all of those interactions.

This is roughly equivalent to when you go to the doctor's office and they let you leave your clothes on when they weigh you. Whatever weight the scale reads — the weight that's measured by the rest of the world — is actually more than your "bare" mass. To get your bare mass, you'd need to subtract the weight of your clothes.

One of the strange things about the universe is that particles and antiparticles constantly pop into existence. For the most part, we don't notice them since they don't last for very long, but when they interact with particles, those interactions can add (or subtract) energy (or what we measure as mass) from other particles.

What's so super about Supersymmetry?

For the Higgs, this correction should be huge, generally of order the Planck Mass — a hugely gargantuan mass (by particle standards) that basically sits at the limits of our ability to reconcile quantum mechanics and general relativity.

To put some numbers on it, suppose the bare mass of the Higgs is something like 2,430,000,000,000,000,125 GeV, the interaction with electrons and positrons might subtract 2,430,000,000,000,000,000 GeV, yielding the observed value of 125 GeV.

The fact that the numbers come so close to matching – but don't exactly match – is too much to accept by chance. This means that the true mass of the of the Higgs would have to be incredibly finely tuned so that the correction and the bare mass almost (but don't exactly) cancel each other to about 1 part in 10^17. The odds of something like that happening in nature by mere chance is so remote as to be laughable.

I only gave you the correction for electrons and positrons, but there are lots of other types of particles out there. Each and every one is going to interact with the Higgs and add a correction to the mass.

There's a weird wrinkle to all of this. We saw earlier that Fermions are associated with a -1, and Bosons got a +1 when you switched two identical particles. Those plus and minus 1's are going to be drafted into service again; they just play a slightly different role this time around.

For each species of Fermion, we subtract from the bare mass to get the observed mass –- that's why I subtracted when talking about electrons –- and with Bosons we add. And for each, we add or subtract roughly the same amount of mass.

But here's the thing: the pluses and minuses don't add up.

What's so super about Supersymmetry?

In the Standard Model at least, there aren't equal numbers of Fermions and Bosons. Including all of the combinations of spin and color, there are 28 different Bosons and 90 different Fermions. If you work through the numbers, this means that the bare mass — the real Higgs mass that you'd measure if you could somehow erase the vacuum of the universe — needs to be something like 62 times the Planck mass in order to see what we see at the LHC. The bare mass and the correction need to match to something like 18 digits.

If you have to do that level of fine tuning, then you are almost certainly cheating. It's a dirty little secret that a lot of what theoretical physicists do is to try to make infinities (or near-infinities) go away.

Why the Higgs needs SUSY

No matter. The solution is simply to hypothesize more particles. This is the central idea of SUSY. SUSY supposes that even Bosons and Fermions are just different sides of the same coin. For every Boson there should be a Fermion and vice-versa. If there are exactly the same number of Fermions and Bosons, then the plus and minus corrections to the Higgs should exactly cancel. It's as though you attach just enough helium balloons to exactly cancel the weight of your clothes when you step onto the scale.

I realize that the solution "make up a bunch of new particles," sounds a) So easy that you don't need an advanced physics degree to come up with it, and b) So silly that it's not clear that it'll do anything, but bear with me for a moment.

What's so super about Supersymmetry?

First off, the idea of coming up with symmetries — in this case between Fermions and Bosons — is really important in physics. The way we understand the weak and electromagnetic forces is ultimately by supposing that the electron and the neutrino (also the up and down quarks) are just different aspects of the same fundamental particle. It's this symmetry that ultimately gives rise to our understanding of the Higgs.

And of course supersymmetry is more than just starting off into space and supposing that there might be lots of other unknown particles out there. There's a fairly hairy mathematical structure to it all; one that predicts interactions between all sorts of particles and their "Superpartners." (I call dibs on the animated series).

Every particle gets a partner of the opposite type. An electron is a Fermion. On the other side is a Boson called a selectron. All of the Bosons get partners with fun, pasta-sounding names. The photon gets a partner called the photino, while the partner of the W Boson, incidentally, is known as the Wino, which if you want to save yourself some embarrassment at your next physicist party, you'll want to pronounce "weeno."

If every particle gets a partner it does seem strange that we've never seen one, doesn't it? Maybe.
One of the generic predictions of supersymmetric models is that the supersymmetric partners should be hundreds or even thousands of times larger than our familiar versions of them. And very massive particles, as you know, don't stick around for long.

There may be a whole bunch of particle states called "neutralinos" which are (as you might guess) electrically neutral. This means that even if we were to make them in an accelerator, they would be very, very tough to detect directly.

And, um, we haven't even detected them indirectly.

Where we are, and what comes next

The initial experimental results from the LHC, as well as experiments to detect SUSY particles directly don't look terribly promising. The problem is that based on everything we know, these particles should have about the same mass as the Higgs, but the current experimental limits suggest that they are, at minimum, several times heavier. That's a pretty big hurtle to clear by just tweaking parameters.

What's so super about Supersymmetry?

Now, the true believers will point out that there are lots of possible SUSY models, many of them fall into a group called the Minimal Supersymmetric Standard Model (MSSM). These simple models may be on life-support, but more complicated schemes could still be viable.

It'd be a shame if SUSY turned out to be wrong, because it would give us huge hints about a lot of outstanding problems.

For example, one of the common assumptions is that the Lightest Superpartner is the neutralino. Hmm…. A massive, abundant particle that's stable because there's nothing for it to decay into? Sounds like Dark Matter. If only SUSY turns out to be a real thing...

Even if supersymmetry is a fact of our universe, it must be at least a little bit broken. If it weren't, all the partners would be the same mass as the originals. But if that were the case, we would have discovered them long ago.

What's so super about Supersymmetry?

One final note. Supersymmetry is often tied to string theory, and, in particular, people will talk about "superstrings," for the simple reason that most versions of string theory and its load of extra dimensions requires supersymmetry as part of the model. The converse does not hold. Supersymmetry could well be right without string theory.

Just putting that out there. Ruling out supersymmetry might help to clear out some of the theoretical cobwebs in physics-land.

Dave Goldberg is a Physics Professor at Drexel University, and is the author of "A User's Guide to the Universe" and the forthcoming "The Universe in the Rearview Mirror," (Dutton, 2013) which will be all about symmetry. In the meanwhile, follow him on twitter, send a question, or become a fan on facebook.