Trial factors for the look elsewhere effect in high energy physics

TL;DR

This paper introduces a quick method to estimate the trial factor, which adjusts the significance of potential signals in high energy physics by accounting for the look elsewhere effect, crucial for accurate discovery claims.

Contribution

It proposes a simple, fast procedure for estimating the trial factor based on Davies' results, improving the efficiency of significance calculations in searches for new resonances.

Findings

Trial factor grows linearly with fixed mass significance asymptotically.

The method provides a practical way to account for the look elsewhere effect.

It enhances the accuracy of significance estimation in high energy physics searches.

Abstract

When searching for a new resonance somewhere in a possible mass range, the significance of observing a local excess of events must take into account the probability of observing such an excess anywhere in the range. This is the so called "look elsewhere effect". The effect can be quantified in terms of a trial factor, which is the ratio between the probability of observing the excess at some fixed mass point, to the probability of observing it anywhere in the range. We propose a simple and fast procedure for estimating the trial factor, based on earlier results by Davies. We show that asymptotically, the trial factor grows linearly with the (fixed mass) significance.