Abstract
The simplest theories where we can understand the origin of the baryon and
lepton number violating interactions are discussed. We discuss the desert
hypothesis in particle physics and the different scenarios where there is no
need to assume it. It is shown that the minimal supersymmetric B-L theory
predicts lepton number violation at the Large Hadron Collider if supersymmetry
is realized at the low scale. We present the BLMSSM where both symmetries, B
and L, can be spontaneously broken at the TeV scale.
