The profile likelihood ratio and the look elsewhere effect in high energy physics

TL;DR

This paper investigates the look elsewhere effect in high energy physics, focusing on the profile likelihood ratio method, proposing a conjecture about its distribution under the null hypothesis, supported by Monte Carlo tests.

Contribution

It introduces a conjecture on the distribution of the likelihood ratio in the presence of the look elsewhere effect, challenging the assumptions of Wilks' theorem.

Findings

Monte Carlo tests support the conjecture

The distribution deviates from Wilks' theorem under the null hypothesis

Implications for significance calculations in broad search intervals

Abstract

The experimental issue of the search for new particles of unknown mass poses the challenge of exploring a wide interval to look for the usual signatures represented by excess of events above the background. A side effect of such a broad range quest is that the significance calculations valid for signals of known location are no more applicable when such an information is missing. This circumstance is commonly termed in high energy physics applications as the look elsewhere effect. How it concretely manifests in a specific problem of signal search depends upon the particular strategy adopted to unravel the sought-after signal from the underlying background. In this respect an increasingly popular method is the profile likelihood ratio, especially because of its asymptotic behavior dictated by one of the most famous statistic result, the Wilks' theorem. This work is centered on the description of the look elsewhere effect in the framework of the profile likelihood methodology, in particular proposing a conjecture about the distribution of the likelihood ratio under the null hypothesis of absence of the signal over the searched mass interval, a condition which is known to violate the conditions of the Wilks' theorem. Several Monte Carlo tests to support the conjecture are presented, as well.