As we have said, supersymmetry (also known as SUSY) is the major prediction of superstring theory at experimentally accessible energies that has not yet been confirmed.
If correct, it implies that every known elementary particle must have a "superpartner." We are quite sure, for reasons I won't go into, that no pair of the known particles are supersymmetry partners of one another. So supersymmetry requires the existence of a new elementary particle for every known one.
As ofter happens, the names are somewhat whimsical: the partners of quarks are called "squarks", the partners of electrons are called "selectrons", the partners of gluons (the Yang-Mills particles that carry the strong nuclear force) are called "gluinos" and so forth.
It is believed that the reason that these particles have not yet been observed is because supersymmetry is a broken symmetry, and as a result the superpartners are heavier than the known elementary particles. Experiments carried out so far have not had particle beams of sufficient energy and intensity to produce them in observable numbers.
Unfortunately, current theoretical ideas are insufficient to accurately predict the superpartner masses, though the way in which these particles interact with one another and with the known particles is predicted precisely.
Even though accurate predictions of the the superpartner masses do not exist, there are three distinct arguments that make qualititative predictions of the masses. All three of them lead to the conclusion that a typical superpartner mass should be in the range of 100 GeV to 1000 GeV. In other words, they should be about 100--1000 times heavier than a proton.
The three arguments are the following:
First, supersymmetry leads to a softening of the short distance singularities of quantum field theory. If we require a sufficient softening so that the Higgs mechanism can break the electroweak symmetry (SU(2) X U(1)) at the observed 300 GeV scale, in which case the Higgs particles have masses of the same order of magnitude, then the scale of supersymmetry breaking must also be approximately the same.
The second argument concerns the unification of the electroweak and strong nuclear forces at very high energy (around $10^{16}$ GeV). One can argue that such a unification is inconsistent with the current experimental data, if one includes the effects of only known particles in the extrapolation, but that it works if supersymmetry partner particles with masses in the 100 GeV to 1000 GeV range are included.
The third argument concerns the possibility that the lightest SUSY particle could be a form of dark matter accounting for a substantial fraction of the mass of the universe. This also requires the same range of masses!

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