  The interpretation of new particle search results involves a confidence level
calculation on either the discovery hypothesis or the background-only ("null")
hypothesis. A typical approach uses toy Monte Carlo experiments to build an
expected experiment estimator distribution against which an observed
experiment's estimator may be compared. In this note, a new approach is
presented which calculates analytically the experiment estimator distribution
via a Fourier transform, using the likelihood ratio as an ordering estimator.
The analytic approach enjoys an enormous speed advantage over the toy Monte
Carlo method, making it possible to quickly and precisely calculate confidence
level results.
