Supersymmetry
In particle physics, supersymmetry is a symmetry that relates bosons and fermions. In supersymmetric theories, every fundamental fermion has a superpartner which is a boson of equal mass, and vice versa. Although supersymmetry has yet to be observed in the real world it remains a vital part of many proposed theories of physics, including various extensions to the Standard Model as well as modern superstring theories.
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2 The supersymmetric standard model 3 Experimental searches 4 Related topics 5 References |
Traditional symmetries in physics are generated by objects that transform under the various tensor representations of the PoincarÃÂé group. Supersymmetries, on the other hand, are generated by objects that transform under the spinor representations. According to the spin-statistics theorem bosonic fields commute while fermionic fields anticommute. In order to combine the two kinds of fields into a single algebra requires the introduction of a Z2-grading under which the bosons are the even elements and the fermions are the odd elements. Such an algebra is called a Lie superalgebra.
The simplest supersymmetric extension of the PoincarÃÂé algebra contains two Weyl spinors with the following (anti)commutation relation:
The supersymmetry algebra
and all other (anti)commutation relations between the Q's and P's vanishing. In the above expression are the generators of translation and are the Pauli matrices.
Under the Standard Model all fundamental particles can be broken down into two groups, fermions that make up matter, and bosons that exchange the forces acting on matter. Due to the physics of the theory, almost all of the behaviour of the universe can be explained based on this handful of particles.
Fermions themselves further break down into three generations, that is, each fermion comes in a variety of three subtypes of increasing mass. For instance one of the most commonly known fermions is the electron, which also has two other less-well-known subtypes, the muon and tau. Fermions also come in two versions for each generation, with differing electric charge. A graph of all the fermions in the Standard Model is quite small. It contains the three generations of quarks and leptons, each broken down into two partners with differing charge.
On the other hand the bosons come in groupings that are nowhere near as "neat", including four distinct types, with subgroups containing anywhere from one to sixteen members. In addition there appears to be no generational structure, the photon only comes in one type for instance, and although it has partners in the W and Z particles, they don't really match up with anything in the fermion side.
The discrepancy between the "clean" fermion side and "messy" boson side has long been one of the most bothersome points of the Standard Model.
It turns out that none of the particles in the Standard Model can be superpartners of each other, so if supersymmetry is correct there must be at least as many extra particles to discover as there are in the Standard Model. The simplest possibility consistent with the Standard Model is the Minimal Supersymmetric Standard Model (MSSM).
A possibility in some supersymmetric models is the existence of very heavy stable particles called neutralinos or photinos which would interact very weakly with normal matter. These would be possible candidates for dark matter.
At present, there is no experimental evidence that supersymmetry exists in the real world. However, there is some indirect evidence which suggests that supersymmetry may be found at energies not too far above those accessible by today's particle accelerators. The search for supersymmetry is one of the primary goals of the Large Hadron Collider (LHC) at the CERN laboratory which is due to open in 2007.
The supersymmetric standard model
Experimental searches
Related topics
References