** **Gluinos and Higgsinos are some of the many undiscovered particles we may find at the Large Hadron Collider (LHC) if a theory called supersymmetry, also known as SUSY, turns out to be true. This theory is built on the Standard Model, the current theoretical model of particle physics.

The Standard Model relies on the Higgs boson to hold true. But even with this boson, physicists know that this model cannot be the final answer as it has a few shortcomings. For example, it fails to provide an explanation for dark matter or why the masses of fundamental particles such as electrons and muons are so different. This theory of supersymmetry is one of the most popular and most promising ways to extend the Standard Model, but it has yet to manifest itself.

SUSY is very popular since it brings lots of harmony in the world of sub-atomic particles. In the Standard Model, there are two types of particles: fermions and bosons. The fermions include quarks and leptons and are the building blocks of matter. These particles have “spin” values of ½. The force carriers are bosons, the other family of particles. They have integer values of spin, that is, 0 or 1.

Supersymmetry would blend fermions and bosons together by associating partners to each particle: a fermion would be paired with a boson, and vice-versa. For example, each quark would come with a “squark,” the name given to the supersymmetric partners of quarks. The squarks would be bosons rather than fermions and would carry spin 0. The same thing goes for leptons. Likewise, the known bosons (gluons, Higgs, W, Z and photons) would come with fermion superpartners with half spin values. These would be the gluinos, Higgsinos, winos, zinos and photinos. A mixture of the force carrier superpartners (all except the gluinos) gives charginos and neutralinos, the latter being particles that would be the perfect candidates for dark matter.

But it is difficult to work with SUSY (nothing personal of course!). Even in its minimal version called the Minimal Supersymmetric Model or MSSM, the theory comes with 105 free parameters. This means each parameter, like the masses of all these particles, is free to take any value it likes.

Think of a parameter as a dimension. Say we need a search party to locate hikers lost anywhere in the Alps. We would have to check every 10 m or so within that huge area. So even when trying to select one single point in a two-dimensional space, the task is daunting. The exact location can be any of a multitude of points within a huge two-dimensional space. Now try to imagine the same situation with a 105-dimensional object! It becomes hopeless.

Adding some reasonable constraints helps such as saying the location can only be on firm ground and not in a lake. This is why theorists have been trying to limit the range of each parameter to reduce the space that would need to be searched to find all these new SUSY particles. A subset of the MSSM model called the Constrained MSSM (CMSSM) model was built leaving only a handful of free parameters. This was achieved by picking somehow arbitrary values for some of these parameters, often guided by taste or guesses for lack of experimental constraints. This is a bit as if in our search for the lost hikers, we decided to ignore Switzerland because we did not like cheese, instead of taking into account the hikers’ interests or habits. But despite all its shortcomings, this model is still largely used.

Since every new theory can only be valid if it can reproduce all known observations, the phenomenological MSSM or pMSSM model was developed using all sorts of measurements done over the past decades in particle physics to constrain the original set of 105 free parameters of the MSSM. With these experimental assumptions, the pMSSM model is reduced to 19 free parameters. There is progress.

Three theorists Alex Arbey, Abdelhak Djouadi and Nazila Mahmoudi, and one experimentalist, Marco Battaglia, form one of the teams who are now going one step further. They are using all available experimental information to see which values of each parameter are still allowed for the different models. This technique requires lots of computing power to test each point of the multi-dimensional space but in the end, one can really see where supersymmetry can still hide.

This method had already revealed that very constrained and specific versions of SUSY like the CMSSM model were getting squeezed into small corners. On the other hand, the pMSSM model has been reduced considerably but still has plenty of space available. Taking into account the recent experimental constraints from the LHC and astrophysics results on dark matter searches, including the recent value obtained by LHCb on Bs mesons decaying into two muons, about 10% of the hundred million possibilities these scientists studied remain valid. And when the measurements on the Higgs-like boson mass and decay rates are taken into account, only 2.5% of the original scenarios in their study survive.

Thanks to this technique of weaving together experimental facts and theoretical knowledge, this team of scientists has been able to reduce a near infinite number of possibilities to only a few percent of what it originally was, making it easier to narrow down the search. Nevertheless, this still leaves plenty of space where one form or another of supersymmetry can exist. We might not be lucky enough to discover SUSY this year but will surely have a good chance at it once the LHC comes back to full power in 2015 after extensive work aimed at increasing the capacity of the accelerator in the coming two years.

Meanwhile, SUSY is still alive and might be kicking around in one point of its now much more confined 105-dimensional space.

Pauline Gagnon

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