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Baryon and Lepton Numbers: Life in the Desert

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.