Searching for periodic signals in kinematic distributions using continuous wavelet transforms

Many models of physics beyond the Standard Model include towers of particles whose masses follow an approximately periodic pattern with little spacing between them. These resonances might be too weak to detect individually, but could be discovered as a group by looking for periodic signals in kinematic distributions. The continuous wavelet transform, which indicates how much a given frequency is present in a signal at a given time, is an ideal tool for this. In this paper, we present a series of methods through which continuous wavelet transforms can be used to discover periodic signals in kinematic distributions. Some of these methods are based on a simple test statistic, while others make use of machine learning techniques. Some of the methods are meant to be used with a particular model in mind, while others are model-independent. We find that continuous wavelet transforms can give bounds comparable to current searches and, in some cases, be sensitive to signals that would go undetected by standard experimental strategies.