Introduction to Supersymmetry


Supersymmetry
-------------

Supersymmetry postulates that each of the particles in 
the Standard Model has a superpartner with a spin that 
differs by 1/2 of a unit.  Each particle from one group 
is associated with a particle from the other, known as 
its superpartner.  Fermions all have a 1/2 of a unit 
of spin, while the bosons have 0, 1 or 2 units of spin. 
Superpartner are identified by the prefix 's' or the 
suffix 'ino'.  Examples,

          Spin    Superpartner   Spin
          ----    ------------   ----
Graviton   2      Gravatino      3/2

fermion   1/2     sfermion        0

gauge      0      gaugino        1/2

Higgs      0      Higgsino       1/2

Supersymmetry is an extension to the Standard Model
that fills in some of the gaps.  In particular it may
resolve an issue called the Hierarchy problem which 
predicts that the Higgs boson should have a much larger
mass.  The extra particles predicted by supersymmetry 
would cancel out the contributions to the Higgs mass 
from their Standard Model partners, making a light 
Higgs boson possible.  The new particles would interact 
through the same forces as Standard Model particles, 
but they would have different masses.  

Second, the lightest supersymmetric particle (LSP) is 
thought to be stable and electrically neutral and to 
interact weakly with the particles of the Standard Model.  
These are exactly the characteristics required for Dark 
Matter, thought to make up most of the matter in the 
Universe and to hold galaxies together.

Finally, supersymmetric theories seem to provide a better
convergence of the coupling constants as the energy scale
increases.  In the Standard Model the coupling constants
'run' as follows:



In Supersymmetry:



Superpartners are heavier than their corresponding
partners which explains why they have yet to be
observed in the laboratory.  The fact that there
is not a perfect symmetry implies that supersymmetry
is not an exact, unbroken symmetry.  The implication 
is that the true symmetry is somehow spontaneously 
broken.

The difference in masses jeopardizes the solution to 
the hierarchy problem because exact cancellation is 
spoiled - but not totally.  The prediction is that 
the mass difference is small enough to still provide 
a high degree of cancellation.  Current estimates
put the mass difference at around 10^GeV at the most.
This is about the mass range accessible to the new
generation of colliders.

Superpartner have the same color charge, weak isospin 
charge, and hypercharge (and consequently electric 
charge) as their partners.

Supergravity
------------

If we demand that supersymmetry be a local (gauge)
symmetry and symmetry is unchanged under a local
transformation at each spacetime point, the local
must include the local Poincare group and therefore
include gravity.  For this reason local supersymmetry
is often referred to as supergravity.  In order to
make supergravity invariant under a local super 
Poincare symmetry group (Poincare + supersymmetry) we 
must now introduce a super gravitational field.  This 
field includes, in addition to the Graviton, the 
Gravitino.  Adding a Gravitino to the picture might 
seem worrisome since it appears that we would be adding 
a new force that modifies the classical theory of 
General Relativity. However, the gravitino is a 
fermion and, because of the Pauli Exclusion Principle, 
their numbers are restricted and long range macroscopic 
effects are avoided.

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