  The fate of R-parity in the context of the minimal supersymmetric standard
model is a central issue which has profound implications for particle physics
and cosmology. In this article we discuss the possibility of testing the
mechanism responsible for the stability of the lightest supersymmetric particle
at the Large Hadron Collider (LHC). The simplest theoretical framework where
R-parity conservation can be explained dynamically allows for two types of B-L
models. In the first scenario the new Higgses decay mainly into two
right-handed neutrinos giving rise to exotic lepton number violating signals
together with displaced vertices. In the second model one could have peculiar
channels with multileptons and/or multiphotons in the final state. In both
cases, the local B-L gauge symmetry is broken at the TeV scale and the
discovery of the new Higgs bosons may be possible at the LHC. We investigate in
detail the production mechanisms for the Higgs bosons relevant for the LHC and
the key decays which would shed light on how R-parity is conserved. These
results may help to understand the link between the cold dark matter of the
universe and the missing energy that could be observed at the LHC if
supersymmetry is realized in nature.
