Searching for a particle of unknown mass and lifetime in the presence of an unknown non-monotonic background

Many extensions to the Standard Model of particle physics hypothesize the existence of new low-mass particles. Typically there are few theoretical constraints on the mass or lifetime of such particles. This requires the experimentalist to perform a search in which both the mass and lifetime of the particle are unknown. Such searches for low-mass particles are complicated by the possible presence of resonances and other non-monotonic backgrounds. This paper presents a simple and fast approach to assigning significance and setting limits in such searches.