Supersymmetry

The success of the unification of the weak- and electromagnetic interactions (see SM post below) soon led to attempts to extend the program to include the strong interaction, i.e. a search for one unified scheme that could describe all three non-gravitational forces (known as Grand Unified Theory) .

However, the GUT program soon ran into serious trouble, with a clutch of ‘no-go’ theorems from mathematicians such as McGlynn, O’Raifeartaigh, Coleman and Mandula showing that such unification could not be achieved using similar gauge methods to that of the electro-weak program. In response, a dramatic new type of symmetry was proposed in the 1970s.

The theory of supersymmetry was a new type of gauge symmetry, and is called ‘super’ in the sense of an ultimate gauge symmetry. Supersymmety (SUSY) supposes a deep connection between two classes of particles that had previously thought to be unrelated – the particles that make up matter (quarks and leptons) and the particles that act as ‘force carriers’ (photons, W and Z bosons ). A very significant difference between the two sets is their spin – quarks and leptons have 1/2 integer spin (called fermions) and obey Fermi-Dirac statistics in consequence. They follow the Pauli Exclusion Principle which states that no two fermions with identical quantum numbers can occupy the same state. ‘Force-carrying’ particles like the photon have integer spin (called bosons ) obey no such rule, and basically behave completely differently.

In essence, supersymmetry posits that every fermion has a corresponding boson sibling and vice versa – in other words, for every quark and lepton there exists a supersymmetric sibling (squarks and sleptons), and every boson also has a supersymmetric partner.

Unfortunately, no-one has ever seen such particles, either in cosmic rays or in particle acceleraor experiments. Hence, if SUSY exists, it must be a broken symmetry, i.e. the supersymmetric partners must have different decay schemes to ‘normal’ particles, and must be much heavier than their ‘normal’ cousins (otherwise we would have seen them). The only way to see if SUSY particles ever existed is to try re-creating them at extremely high energies in particle accelerators (much as we create anti-particles). This is one of the things the new collider at CERN was built to look for.

That said, theoreticians claim that there are indirect hints that SUSY , or something like it, might be right. The first is the convergence of the three non-gravitational forces. While these forces appear completely different at low energy, they have a different energy dependence, and may in fact converge at high enough energies. However, detailed calculations show that they converge to a point only if supersymmetry is allowed for. Unfortunately, this is a purely theoretical conjecture – you can see from the diagram below that the convergence is expected to occur at energies way beyond the reach of current accelerators.

GUT convergence including supersymmetry

The second is a hint from cosmology – we are pretty sure that well over 2/3 of the matter of the universe is ‘dark matter’, i.e. only seen by its gravitational effect (see post below). Such matter must be massive and yet weakly interacting (WIMPS) – an idea that fits supersymmetric particles very nicely. In fact, the favoured candidate for dark matter is the lightest SUSY particle, the neutralino (see post below).

Hence the search for SUSY particles at CERN, and the search for Dark Matter in cosmology are experiments that complement each other. Progress on either front will probaby have implications for the other, a fantastic convergence of particle physics and cosmology.