Supersymmetry

Supersymmetry is a principle that a theory might have. It is a transformation, or, a relationship between the two families of particles: bosons, which have a whole integer value spin, and fermions, which have a half integer value spin. Each boson will have a superpartner fermion and vice-versa. 

Abdus Salam once said: "Supersymmetry is the ultimate proposal for a complete unification of all particles."

Supersymmetry is the prediction that for each particle, there is a partner particle. These partner particles' spin would differ, by a half integer. This would be a kind of theoretical extension to the Standard Model, that could hopefully answer some questions, since, as we know, the Standard Model is, as even acknowledged by it's proponents, an incomplete theory. The Standard Model, does not include gravity, and does not give a definite and sufficient mechanism for mass generation. 

If supersymmetry is correct, than the Large Hadron Collider, should find these superpartners. However, there is no evidence at this time.

Sparticles were never observed in experiments. There has never been observed a spin-0 partner to the spin-1/2 electron. There is not a single shred of evidence of superpartners yet. However, many theorists believe that sparticles exist at very high energies, such as those that existed at the moment of the Big Bang.