Low energy supersymmetry with baryon and lepton number gauged

We investigate the spontaneous breaking of the Baryon ($B$) and Lepton ($L$) number at the TeV scale in supersymmetric models. A simple extension of the minimal supersymmetric standard model where $B$ and $L$ are spontaneously broken local gauge symmetries is proposed. The $B$ and $L$ symmetry breaking scales are defined by the supersymmetry breaking scale. By gauging $B$ and $L$, we understand the absence of the baryon and lepton number violating interactions of dimension four and five in the minimal supersymmetric standard model. Furthermore, we show that even though these symmetries are spontaneously broken there are no dangerous operators mediating proton decay. We discuss the main properties of the spectrum, the possible baryon number violating decays and the implications for the dark matter candidates. In this model, one can have lepton number violating signals from the decays of the right-handed neutrinos and baryon number violating signals from the decays of squarks and gauginos without conflict with the bounds coming from proton decay, $n-\overline{n}$ oscillations and dinucleon decays.