Signs of supersymmetry and thus dark matter at CERN The Large Hadron Collider at CERN has just re-started after a two year pause and is now running at unprecedented levels of 6.5 TeV, with collisions that will release up to 13.5 TeV. With this increase in energy, far more massive particles will be able to be created, than was physically possible 3 years ago. The main task will now be to try to prove the existence of the supersymmetry hypothesise, which could then provide the solution to the nature of dark matter.
So my question is: what signs of supersymmetry are they hoping to find at CERN (i.e. what constitutes a sign of supersymmetry) and how will this relate to the solution to the nature of dark matter?
 A: Although Supersymmetry (SUSY) - under certain assumptions - predicts the existence of Dark Matter (DM) candidate, the signals for DM are not specific to SUSY.

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*Fist, how to detect DM at the LHC:
DM will not be detected by the experiments directly as it is believed (reasonable assumption) to not interact with regular matter. Therefore the only way of spotting it is with the so-called missing energy (or missing $p_T$, transverse momenta), which indicates neutral particles are being produced. There is nothing magical about producing invisible matter, look for example at neutrinos. Insofar, neutrinos are the only components of invisible matter produced at colliders, so for example the Large Electron Positron collider (LEP) concluded, assuming the remaining Standard Model (SM) particles discovered until that time, that there are 3 flavours/families of Neutrinos. This is a remarkable achievement and is in agreement with the cosmological bounds on effective light (below the weak scale mass) neutrinos. It's a necessary condition for Dark matter to be discovered if there is missing energy that cannot be accounted solely by the SM neutrinos. It is not enough to escape the collider detection to assert it's DM, it also has to be stable at cosmological scales ($t \gtrsim 10^{25} \sec$), and so a positive signal from collider detectors will have to be substantiate by other experiments (the so-called direct searches, for example).


*Signs of SUSY.
The above requirement for DM candidate does not imply SUSY, what implies SUSY is the Supersymmetric particle spectrum. SUSY predicts a bunch of new fields with SM quantum numbers repeated to those of current known matter, but with mismatching spins (so an electron as scalar partner, and a gauge boson a fermion partner, etc). This is the only and unambiguous sign for SUSY. The only way to discover SUSY is to see this replication of SM states with different spins.


*How to reconcile the two?
Although most SUSY models predict a DM candidate, there are many SUSY models without DM and this has to be explained through some other physics. In order for SUSY to be responsible for DM, the SUSY model has to have what is known to be R-parity (or some sort of matter parity) and in which case the lightest SUSY particle (LSP) does not decay and, if neutral, has all the ingredients to be DM. If this happens (which can be checked by how the SUSY partners interact) then SUSY immediately has a DM candidate. If not, then SUSY by itself is not sufficient to explain DM and one has to go beyond, like Strings which provide Moduli and Axions, the later being generally considered a good DM candidate.
Bottom line is, the LHC can give positive DM candidate signals that will still have to be checked for realistic DM. Regarding SUSY, if the full SUSY spectrum is discovered it's likely that SUSY exists, but the relation to DM is not immediate and is, so far, model dependent.
References
http://pdg.lbl.gov/2012/reviews/rpp2012-rev-light-neutrino-types.pdf
http://en.wikipedia.org/wiki/Dark_matter#Detection
http://en.wikipedia.org/wiki/R-parity
http://en.wikipedia.org/wiki/Lightest_Supersymmetric_Particle
