Detection of a small shift in a broad distribution

TL;DR

This paper evaluates statistical techniques for detecting small shifts in broad data distributions through Monte Carlo simulations, motivated by neutrino timing experiments, emphasizing the importance of precise shift detection despite large fluctuations.

Contribution

It introduces and assesses statistical methods capable of identifying tiny shifts within broad distributions, relevant for high-precision physics experiments.

Findings

Monte Carlo simulations demonstrate method effectiveness

Small shifts can be detected despite large fluctuations

Methods remain relevant after the physical result was withdrawn

Abstract

Statistical methods for the extraction of a small shift in broad data distributions are examined by means of Monte Carlo simulations. This work was originally motivated by the CERN neutrino beam to Gran Sasso (CNGS) experiment for which the OPERA detector collaboration reported a time shift in a broad distribution with an accuracy of $\pm 7.8\,$ns, while the fluctuation of the average time turns with $\pm 23.8\,$ns out to be much larger. Although the physical result of a big shift has been withdrawn, statistical methods that make an identification in a broad distribution with such a small error possible remain of interest.