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CERN | Geneva | Switzerland

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Supersymmetry: a tantalising theory

This is the second part of a series of three on supersymmetry, the theory many believe could go beyond the Standard Model. First I explained what is the Standard Model and showed its limitations. I now introduce supersymmetry and explain how it would fix the main flaws of the Standard Model. Finally, I will review how experimental physicists are trying to discover “superparticles” at the Large Hadron Collider (LHC) at CERN.

Theorists often have to wait for decades to see their ideas confirmed by experimental findings. This was the case for François Englert, Robert Brout and Peter Higgs whose theory, elaborated in 1964, only got confirmed in 2012 with the discovery of the Higgs boson by the LHC experiments.

Today, many theorists who participated in the elaboration of what is now known as supersymmetry, are waiting to see what the LHC will reveal.

Supersymmetry is a theory that first appeared as a mathematical symmetry in string theory in early 1970s. Over time, several people contributed new elements that eventually led to a theory that is now one of the most promising successors to the Standard Model. Among the pioneers, the names of two Russian theorists, D. V. Volkov and V. P Akulov, stand out. In 1973, Julius Wess and Bruno Zumino wrote the first supersymmetric model in four dimensions, paving the way to future developments. The following year, Pierre Fayet generalized the Brout-Englert-Higgs mechanism to supersymmetry and introduced superpartners of Standard Model particles for the first time.

All this work would have remained a pure mathematical exercise unless people had noticed that supersymmetry could help fix some of the flaws of the Standard Model.

As we saw, the Standard Model has two types of fundamental particles: the grains of matter, the fermions with spin ½, and the force carriers, the bosons with integer values of spin.

The mere fact that bosons and fermions have different values of spin makes them behave differently. Each class follows different statistical laws. For example, two identical fermions cannot exist in the same quantum state, that is, something -one of their quantum numbers – must be different. Quantum numbers refer to various properties: their position, their charge, their spin or their “colour” charge for quarks. Since everything else is identical, two electrons orbiting on the same atomic shell must have different direction for their spin. One must point up, the other down. This means at most two electrons can cohabit on an atomic shell since there are only two possible orientations for their spins. Hence, atoms have several atomic shells to accommodate all their electrons.

On the contrary, there are no limitations on the number of bosons allowed in the same state. This property is behind the phenomenon called superconductivity. A pair of electrons forms a boson since adding two half spins gives a combined state with a spin of 0 or 1, depending if they are aligned or not. In a superconductor, all pairs of electrons can be identical, with exactly the same quantum numbers since this is allowed for combined spin values of 0 or 1. Hence, one can interchange two pairs freely, just like two grains of sand of identical size can swap position in quick sand, which makes it so unstable. Likewise, in a superconductor, all pairs of electrons can swap position with others, leaving no friction. An electric current can then flow without encountering any resistance.

Supersymmetry builds on the Standard Model and associates a “superpartner” to each fundamental particle. Fermions get bosons as superpartners, and bosons get associated with fermions. This unifies the building blocks of matter with the force carriers. Everything becomes more harmonious and symmetric.


Supersymmetry builds on the Standard Model and comes with many new supersymmetric particles, represented here with a tilde (~) on them. (Diagram taken from the movie “Particle fever” reproduced with permission from Mark Levinson)

But there are other important consequences. The number of existing fundamental particles doubles. Supersymmetry gives a superpartner to each Standard Model particle. In addition, many of these partners can mix, giving combined states such as charginos and neutralinos

This fact has many implications. First major consequence: the two superpartners to the top quark, called the stops, can cancel out the large contribution from the top quark to the mass of the Higgs boson. Second implication: the lightest supersymmetric particle (in general one of the mixed states with no electric charge called neutralino) has just the properties one thinks dark matter should have.

Not only supersymmetry would fix the flaws of the Standard Model, but it would also solve the dark matter problem. Killing two huge birds with one simple stone. There is just one tiny problem: if these supersymmetric particles exist, why have we not found any yet? I will address this question in the next part in this series.

Pauline Gagnon

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5 Responses to “Supersymmetry: a tantalising theory”

  1. Stam Nicolis says:


    There’s a typo: The sentence

    “the two superpartners to the top quark, called the stops,” should read, rather,

    “the superpartner of the top quark, called the stop,”

  2. noobster says:

    Sorry, this is a dumb question, but if only two electrons can occupy an atomic shell then how come the p, d, f shells accommodate more than 2 electrons?

    • chris says:

      Not a dumb question – the reason is that each energy shell (other than the lowest, s) is composed of multiple orbitals. The Pauli Exclusion Principle implies the rule mentioned here – that no more than two electrons can occupy the same orbital. But while the s shell only has 1 orbital, the p shell has 3, allowing the p shell to carry a total of six electrons; the d shell has 5 orbitals -> 10 electrons; the f shell has 7 orbitals -> 14 electrons. Really, this all relates back to quantum numbers; here’s a good link for more about them: http://www.angelo.edu/faculty/kboudrea/general/quantum_numbers/Quantum_Numbers.htm

  3. Brian Goldwyn says:

    This is very cool! I never heard about neutralinos before – it’s amazing that following a pattern can theoretically create a particle that just so happens to fit in with an observed yet unknown phenomena of dark matter! The particle wasn’t even invented to describe dark matter – that just happened by accident. Amazing!

  4. Cassy says:

    Hi Pauline,
    Thanks for sharing the article. Waiting eagerly for the next part.

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