Reconstructing ATLAS SU3 in the CMSSM and relaxed phenomenological supersymmetry models

Assuming that the LHC makes a positive end-point measurement indicative of low-energy supersymmetry, we examine the prospects of reconstructing the parameter values of a typical low-mass point in the framework of the Constrained MSSM and in several other supersymmetry models that have more free parameters and fewer assumptions than the CMSSM. As a case study, we consider the ATLAS SU3 benchmark point with a Bayesian approach and with a Gaussian approximation to the likelihood for the measured masses and mass differences. First we investigate the impact of the hypothetical ATLAS measurement alone and show that it significantly narrows the confidence intervals of relevant, otherwise fairly unrestricted, model parameters. Next we add information about the relic density of neutralino dark matter to the likelihood and show that this further narrows the confidence intervals. We confirm that the CMSSM has the best prospects for parameter reconstruction; its results had little dependence on our choice of prior, in contrast to the other models that we study where the situation is less clear. By comparing parameter reconstruction we find that sometimes gaugino mass unification, rather than having fewer free parameters, is critical. We also study prospects for evaluating the relic density of neutralino dark matter from LHC data alone and for direct detection searches with information from both LHC data and the relic density of dark matter. Finally we perform a brief comparison of parameter and relevant mass reconstruction in the models that we study.