Asymptotic formulae for likelihood-based tests of new physics

TL;DR

This paper develops asymptotic formulae for likelihood-based tests in high energy physics, enabling more accurate discovery claims and confidence intervals while accounting for systematic uncertainties, and introduces the concept of the Asimov data set for median sensitivity estimation.

Contribution

It provides explicit asymptotic distributions for likelihood-based test statistics and introduces the Asimov data set for simplified sensitivity analysis.

Findings

Derived explicit asymptotic distributions for test statistics.

Justified the use of the Asimov data set for median sensitivity.

Enhanced methods for systematic uncertainty incorporation.

Abstract

We describe likelihood-based statistical tests for use in high energy physics for the discovery of new phenomena and for construction of confidence intervals on model parameters. We focus on the properties of the test procedures that allow one to account for systematic uncertainties. Explicit formulae for the asymptotic distributions of test statistics are derived using results of Wilks and Wald. We motivate and justify the use of a representative data set, called the "Asimov data set", which provides a simple method to obtain the median experimental sensitivity of a search or measurement as well as fluctuations about this expectation.