  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.
