Likelihood analysis of the next-to-minimal supergravity motivated model

In anticipation of data from the Large Hadron Collider (LHC) and the potential discovery of supersymmetry, in this work we seek an answer to the following: What are the chances that supersymmetry will be found at the LHC? Will the LHC data be enough to discover a given supersymmetric model? And what other measurements can assist the LHC establish the presence of supersymmetry? As a step toward answering these general questions, we calculate the odds of the next-to-minimal version of the popular supergravity motivated model (NmSuGra) being discovered at the LHC to be 4:3 (57 ). We also demonstrate that viable regions of the NmSuGra parameter space outside the LHC reach can be covered by upgraded versions of dark matter direct detection experiments, such as super-CDMS, at 99 confidence level (assuming uniform priors). Our qualitative conclusion is robust against variation of the Bayesian prior. Due to the similarities of the models, we expect very similar results for the constrained minimal supersymmetric standard model (CMSSM).