Expected Signal Observability at Future Experiments

Several methods to quantify the ''significance'' of an expected signal at future experiments have been used or suggested in literature. In this note, comparisons are presented with a method based on the likelihood ratio of the ''background hypothesis'' and the ''signal-plus-background hypothesis''. A large number of Monte Carlo experiments are performed to investigate the properties of the various methods and to check whether the probability of a background fluctuation having produced the claimed significance of the discovery is properly described. In addition, the best possible separation between the two hypotheses should be provided, in other words, the discovery potential of a future experiment be maximal. Finally, a practical method to apply a likelihood-based definition of the significance is suggested in this note. Signal and background contributions are determined from a likelihoo d fit based on shapes only, and the probability density distributions of the significance thus determined are found to be of a Gaussian shape even with small statistics.