  In this thesis we study the phenomenology of an anomalous U(1) extension of
the MSSM. We briefly introduce the concept of Supersymmetry and describe the
MSSM, then we introduce our extended model, describing its main properties.
  Then it starts the original part of the thesis. First there is the study of
the model in the most general case, in which there is mixing between the SM
U(1) and the anomalous U(1). This is followed by the calculation of all the
vertices and the amplitudes that are of interest for the phenomenology that we
are going to study.
  After describing in details how the Boltzmann Equation gives the relic
density of particle species, we use it and the amplitudes of our model already
calculated to study if the neutralinos introduced by our model can be viable
candidates to describe the Dark Matter relic density. We have found that this
is the case only if the anomalous candidate coannihilates with a MSSM
neutralino.
  In the case of no mixing between the U(1)s we have obtained this results
performing analytical calculations, whom results we show for many mass gaps.
  To obtain the same result in the mixing case we have modified the DarkSUSY
package. This has also permitted us to obtain more precise informations about
the dependence of the relic density on the various free parameters of the
model. We show many plots containing these results.
  In the last part of the thesis we study the Asymmetry at the LHC for our
model. We start introducing the Forward-Backward Asymmetry then we move on to
describe how it can be utilized at the LHC. We introduce different possible
definitions and describe their properties, then we calculate their predicted
values in our model. Finally we explain how these results could be used to
impose constraints over theoretical models that describe beyond the Standard
Model physics.
