Using the Profile Likelihood in Searches for New Physics

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  • 10 July 2010
Abstract
We discuss the use of the profile likelihood in particle physics searches for processes whose existence has not been established. The methods allow one to quantify the significance of an observed signal or to establish limits on the parameters of possible signal models. The use of the profile likelihood incorporates systematic uncertainties when their effects are related to nuisance parameters. Approximate sampling distributions for test statistics are determined using results due to Wilks and Wald, which allow one to determine the significance with which one may reject a given hypothesized model. We motivate and justify the use of a representative data set, the "Asimov data set", to find the median discovery and exclusion significance, and provide simple methods for obtaining the expected statistical variation in the form of error bands for the experimental sensitivity.

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