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

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