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 traditional significance calculations valid for signals of known location are no more applicable when such an information is missing. In this note the specific signal search approach via observation windows sliding over the range of interest is considered; in the assumptions of known background and of fixed width of the exploring windows the statistical implications of such a search scheme are described, with special emphasis on the correct significance assessment for a claimed discovery.
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