$B$ and $L$ at the supersymmetry scale, dark matter, and $R$-parity violation

We present a simple theory where baryon and lepton numbers are spontaneously broken at the supersymmetry scale. In this context $R$ parity must be spontaneously broken but the theory still contains a stable field which can play the role of the cold dark matter of the Universe. We discuss the spectrum of the theory, the properties of the dark matter candidate and the predictions for direct detection experiments. This theory provides a concrete example of exotic supersymmetric signatures associated with having the simultaneous presence of $R$-parity-violating and missing energy signals at the Large Hadron Collider.

Figure 1

Predictions for the elastic nucleon-dark matter cross section for different values of the dark matter mass when $0.11<{\Omega }_{\tilde{X}}{h}^2<0.13$.

Figure 2

Allowed values for the gauge coupling and the dark matter mass when $0.11<{\Omega }_{\tilde{X}}{h}^2<0.13$ and $M_{Z_1}=2,3,4\mathrm{TeV}$.