Significance of an excess in a counting experiment: assessing the impact of systematic uncertainties and the case with Gaussian background

Understand

Several experiments in high-energy physics and astrophysics can be treated as on/off measurements, where an observation potentially containing a new source or effect ("on" measurement) is contrasted with a background-only observation free of the effect ("off" measurement).

• In counting experiments, the significance of the new source or effect can be estimated with a widely-used formula from [LiMa], which assumes that both measurements are Poisson random variables.
• In this paper we study three other cases: i) the ideal case where the background measurement has no uncertainty, which can be used to study the maximum sensitivity that an instrument can achieve, ii) the case where the background estimate $b$ in the off measurement has an additional systematic uncertainty, and iii) the case where $b$ is a Gaussian random variable instead of a Poisson random variable.
• The latter case applies when $b$ comes from a model fitted on archival or ancillary data, or from the interpolation of a function fitted on data surrounding the candidate new source/effect.