Multiplicative scale uncertainties in the unified approach for constructing confidence intervals

Abstract

We have investigated how uncertainties in the estimation of the detection efficiency affect the 90% confidence intervals in the unified approach for constructing confidence intervals. The study has been conducted for experiments where the number of detected events is large and can be described by a Gaussian probability density function. We also assume the detection efficiency has a Gaussian probability density and study the range of the relative uncertainties ${\sigma }_{\epsilon }$ between 0 and 30%. We find that the confidence intervals provide proper coverage over a wide signal range and increase smoothly and continuously from the intervals that ignore scale uncertainties with a quadratic dependence on ${\sigma }_{\epsilon }$.

22 pages, 7 figures, 2 tables

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