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Physics + MathPhysics & Math

Supersymmetry: Looking in Nature's Mirror

ByDon LincolnThe Nature of RealityThe Nature of Reality


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recent buzz over the discovery of a new boson that might be the long-sought quantum of the Higgs field has led some to forget that the
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Large Hadron Collider at CERN isn’t a single-purpose facility. Two large experiments each engage approximately 3,000 physicists in a concentrated effort to better understand the rules that govern the universe in which we live. These collaborations can study many different phenomena. One of the most tantalizing of these phenomena is called supersymmetry—and it could pick up where the Higgs left off.

There are many mysteries remaining in physics. While the Standard Model states that the Higgs boson gives subatomic particles their mass, it is quite silent on the specific masses held by each particle. Further, it doesn’t explain why so many different types of particles exist, nor does it explain why there are three forces and not two or 20.

Subatomic particles have a property called spin which can be usefully (and misleadingly) imagined as each particle being a tiny spinning ball, though the reality is that spin is an inherent property of these particles in the same way that electric charge is. Particles are divided into two classes based on their spin: Particles with half-number spin (1/2, 3/2, 5/2 and so on) are called fermions, and particles with whole-number spin are called bosons.

Supersymmetry proposes a new rule to govern the relationship between fermions and bosons. According to supersymmetry, the equations that describe the universe should work in exactly the same way if all fermion and boson terms are swapped. This implies that, for every particle known in the Standard Model, there should be an as-yet-undiscovered cousin particle. These cousin particles are identical to the known particles in every way except that they have different spin.

If supersymmetry is right, then the existing fermion quarks have cousin bosons called “squarks”; the lepton has a supersymmetric cousin called a slepton. For bosons, the naming convention is a little different: The bosons of the standard model (the gluon, photon and W and Z boson) have supersymmetric fermion cousins called the gluino, photino, wino and zino.

Though none of these particles has yet been observed, their very obscurity does offer us one important insight: If supersymmetry exists, it is not, in fact, symmetric. Recall that I said that the supersymmetric cousins of the familiar particles of the Standard Model were the same in every way except for their spin. This means that the selectron would have the same mass as the familiar electron and the up squark would have the same mass of the up quark. However, were this true, we would have discovered them already. Given that we haven’t, we can categorically say that supersymmetry in its ideal form has already been falsified.

However it could be that supersymmetry is mostly true, but “broken.” In the same way that an imperfect top might spin reasonably well, only to wobble a bit and end with a preferred side always touching the ground when it stops, perhaps the universe might have a supersymmetry that is mostly true. Just what mechanism breaks the symmetry between the Standard Model particles and the supersymmetric cousins is not known, although many ideas have been proposed.

So with this additional consideration, you are to be forgiven if you are suspicious of the whole idea. What is the reason for the interest in the idea of supersymmetry? Why have over ten thousand scientific papers (both experimental and theoretical) been written on the subject?

While there are several reasons to find the idea intriguing, one topical example is the way in which supersymmetry is thought to be linked to the Higgs boson. While we remain unsure if the boson we found in July is the Higgs boson, the new boson has a mass of about 125 GeV, or about 133 times heavier than a proton. This is an utterly unnatural value for the mass of the Higgs boson.

Why unnatural? The Higgs boson gains its own mass (in part) through its interaction with the other subatomic particles: the quarks and leptons and force carrying bosons. These particles should have a huge influence on the mass of the Higgs—on the scale of 10 15 GeV. That’s over ten trillion times the observed mass of the new boson. So why isn’t the Higgs weighing in at that enormous mass?

First, we are helped because the contribution from the fermions and bosons are of opposite sign, so they can cancel each other out. But without invoking supersymmetry, it seems pretty suspicious that they would be so close in value. It’s uncanny, like a big bank simultaneously taking in a deposit of about a trillion dollars and making a loan of almost exactly the same amount down to a few bucks.

Supersymmetry can explain this quite easily, though. After all, for each particular fermion (say an electron), there is a corresponding boson (a selectron). Given the symmetry and the fact that fermions and bosons contribute with opposite signs, it is easier to see how these two corresponding particles could cancel each other out exactly. If supersymmetry were in fact perfectly symmetric, they would cancel each other perfectly and mass of the Higgs boson would be caused solely by its interaction with other Higgs bosons.

This example is but one in the myriad of phenomena which can be explained by supersymmetry. You should remember that we don’t know that supersymmetry is actually present in the universe; just because it works on paper doesn’t make it real. It makes it a cool idea. However scientists at the Large Hadron Collider are hot on supersymmetry’s trail. If supersymmetry is the answer to why the mass of the Higgs boson is small but not zero, we will find it at the LHC.

Go Deeper
Editor’s picks for further reading

Nature’s Blueprint: Supersymmetry and the Search for a Unified Theory of Matter and Force
Theoretical astrophysicist Dan Hooper’s book on supersymmetry and the LHC’s role in the search for evidence of supersymmetry.

Scientific American: Is Supersymmetry Dead?
Davide Castelvecchi asks what it will mean for physics if the LHC does not turn up evidence of supersymmetry.

Supersymmetry: Unveiling the Ultimate Laws of Nature
Physicist Gordon Kane’s accessible 2001 book on supersymmetry.

This project/research was supported by grant number FQXi-RFP-1822 from the Foundational Questions Institute and Fetzer Franklin Fund, a donor-advised fund of Silicon Valley Community Foundation.