Supersymmetry

Birth of the supersymmetry

Theorem No-Go of Coleman and Mandula

The standard model of the physics of the particles in entirely was almost built thanks to the concepts of symmetry and invariance.

The history of the supersymmetry starts in the Années 1960. At this time, the whole of symmetries considered belonged to the group of Poincaré. Curious physicists naturally put the question to know if this group could be wide. One in particular was interested in the extension of symmetry $SU (3)$ of savor (not to be confused with $SU (3)$ of color) to $SU (6)$ within a relativistic framework. All the attempts fail, and a theorem No-go breaks all the hopes.

Coleman and Mandula publish their article in 1967. They show that the group of Poincaré is the most general group of symmetry of the matrix S. Their demonstration is based on the following assumptions:

For a mass M given, there exists a finished number of type of particles of mass lower than M
the amplitudes corresponding has elastic scatterings are analytical functions of the variables S (energy. center of mass) and scattering angle.
Is $|p_1, p_2 \ rangle$ a state with two particles, $S|p_1, p_2 \ rangle \ neq |p_1, p_2 \ rangle$ except for certain values isolated from S.
the operators of symmetry is defined through their relations of commutation, those form an algebra of Dregs.

It is the last point which will make it possible to circumvent No-go theorem in order to introduce the supersymmetry, in a super algebra of dregs.

Phenomenologic interest

Tally mathematical

Description

If one postulates the invariance theory under the algebra of super Poincaré, which extends the Algèbre of Poincaré on which is based the usual physics of the particles, then one can build extensions of the standard model which incorporate the supersymmetry naturally (see the minimal supersymmetric standard Modèle (ms).

The Secteur of Higgs, which is responsible for the generation of the nonnull masses for the matter in the standard model, is also extended to at least 5 bosons of Higgs within the framework of the ms.

In 2006, however, no “super-partner” of the known particles was still observed. If it exists, the SUSY must thus be a broken symmetry: this implies in particular that the “super-partners” must have masses different from those of their partners and that it is necessary to consider phenomena on high scales of energy in order to restore and see reappearing this symmetry. The startup, planned for 2008, of LHC should make it possible to check or invalidate the assumption of the existence of the supersymmetry.

In spite of the fact that the number of particles is doubled, the SUSY has many advantages:

By postulating the existence of “super-partner” about the TeV, the unification of the strong Interaction, weak and electromagnetic becomes possible on a scale of energy about 10¹⁶ GeV (scale of Great unification);
This theory also makes it possible to explain naturally why the mass of Higgs can be low (in lower part of TeV);
It also makes it possible to explain the black Matière of our universe by the means of the neutralino S (stable supersymmetric particles interacting very slightly with the matter).
Within the framework of the Cosmology, it makes it possible to explain the weakness of the cosmological Constante.

Random links: