Trial factors or the look elsewhere effect in high energy physics

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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". Here we attempt to quantify this effect in terms of a trial factor, which is the ratio of the probability of observing the excess at some fixed mass point, to the probability of observing it anywhere in the range. We show that, under some approximations, this trial factor grows linearly with the (fixed mass) significance.

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