This is the text of the mini-lecture on Supersymmetry that nuclear physicist Filip Moortgat kindly gave us during our visit to CERN and the Large Hadron Collider last week.

Filip Moortgat: Supersymmetry stands out among all the other Beyond Standard Model theories (like extra dimensions and so on). It’s particularly interesting because it answers multiple things at the same time. I would say that most other extensions of the Standard Model solve one problem but not five like supersymmetry.

The first problem: because it connects the internal property of a particle to spacetime, it actually opens a way of gravity entering the Standard Model. As you know, the main problem with the Standard Model is that gravity is not in there. So one of the major forces that we know exists is not in there. Nobody has succeeded to make gravity part of it in a way that is consistent. People hope that supersymmetry can do it, although we’re not there yet.

The second problem is called the hierarchy problem. What that means is that you have a base mass for a particle and then you have corrections to it from all the other particles. What happens is that if you don’t have any other particles beyond the Standard Model particles you get corrections that become gigantic. What you need to do is tune the base mass and these corrections so that you get the mass that we measured for the Higgs Boson or for the w and z bosons. It’s like 10^31 minus 10^31 is a 100 type of tuning, and we find it unnatural. It’s ugly mathematics. In supersymmetry, you get automatic cancelation of these big corrections: You get a big one and then you get minus the big one (the same correction but with a minus in front of it), it cancels out and it’s pretty, it’s beautiful.

The third thing is dark matter, a big problem. 85 procent of the matter in the universe is dark matter (if you also include the energy in the universe, you get different numbers). And the lightest stable supersymmetry particle is actually a perfect candidate for dark matter, in the sense that it has all the properties and if you compute how much you expect it’s exactly what you observe in the universe. It works great. It doesn’t mean that it’s true, it would work great if you could find it.

And then there’re more technical arguments that make things connect together in nicer ways than before. Normally, the electric symmetry is broken in the way that everything becomes zero. All the masses would be zero, the universe would just be floating particles that wouldn’t connect to each other, it would be very boring. But that’s not what happened. To show what actually happened you need to drive one mass squared term negative, which is kind of weird but that is what supersymmetry does automatically! Because the top quark mass is so heavy. Heavier than all the other quarks. For me it’s the most beautiful extension of the Standard Model that gives you a lot of solutions to problems in one go.

The problem is that we haven’t seen anything, yet! We have been looking for it for a long time and we have absolutely zero evidence. We now have reasons to believe that it’s not as light as we have originally thought, that it’s a little bit heavier. Which is not a problem. The LHC has a certain mass range, for supersymmetry it’s typically up to a couple of TeV. But it could be 10 TeV and then we couldn’t get there, we can only get up to 2 or 3 TeV. It could be factor 10 heavier than we think!

This why we are starting to discuss the planning of the Future Collider that will be able to go up the spectre of 10 TeV in mass, for supersymmetry and other theories. There’re several proposals, some of them are linear colliders, but my favourite one is a 100 km circular collider which will connect to the LHC, so that we have one more ring. That ring will actually go under the lake and that would be quite challenging, but in my opinion – although we don’t have any guarantee – we will then have a very good shot, at least in terms of supersymmetry. At the LHC we also have a good shot but don’t have enough reach that we need to really explore the supersymmetry.

When we use conservation of energy and momentum at the collision point, what we do is we measure everybody, we sum it all up and what we need is we need to get the initial state. If something is lacking, then we know there’s something invisible going on. It could be neutrinos, or neutralinos, or it could be something else. So we have to look at the properties and the distributions to figure out exactly what we’re seeing. It’s not a direct detection but it’s a direct derivation if you want, from not seeing something, from lacking something, that we can still say it is consistent with neutralinos.

How do you know if it’s neutrinos or neutralinos?

Neutrinos we know well by now so we know what to expect with neutrinos. Otherwise it could be neutralios but it could be something else. And then to actually prove that it’s neutralinos we have a long program of work.

And is that mainly math?

No, it’s everything. It needs all the communities to work together, because we need to measure certain properties, distributions with the detector and we will need the theoretical ideas on how to connect these measurements to the properties of the particle. So we will need both the mathematical part and the experimental part. Translating the mathematics into the particle predictions, we will need all of that.