Likelihood approach to the first dark matter results from XENON100

Many experiments that aim at the direct detection of dark matter are able to distinguish a dominant background from the expected feeble signals, based on some measured discrimination parameter. We develop a statistical model for such experiments using the profile likelihood ratio as a test statistic in a frequentist approach. We take data from calibrations as control measurements for signal and background, and the method allows the inclusion of data from Monte Carlo simulations. Systematic detector uncertainties, such as uncertainties in the energy scale, as well as astrophysical uncertainties, are included in the model. The statistical model can be used to either set an exclusion limit or to quantify a discovery claim, and the results are derived with the proper treatment of statistical and systematic uncertainties. We apply the model to the first data release of the XENON100 experiment, which allows one to extract additional information from the data, and place stronger limits on the spin-independent elastic weakly interacting massive particles nucleon scattering cross section. In particular, we derive a single limit, including all relevant systematic uncertainties, with a minimum of $2.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}44}\text{ }\text{ }{\mathrm{cm}}^{2}$ for weakly interacting massive particles with a mass of $50\text{ }\text{ }\mathrm{GeV}/{c}^{2}$.