A Likelihood Ratio Framework for Highly Motivated Subdominant Signals

In particle physics and cosmology, distinguishing subtle new physics signals from established backgrounds is a fundamental and persistent challenge for phenomenologists. This paper discuss a simple and robust statistical framework to evaluate the compatibility of highly motivated (HM) theoretical models with the residuals of experimental results, focusing on scenarios where the data appear consistent with background predictions. A likelihood ratio test is developed that compares null and alternative hypotheses, emphasizing cases where new physics introduces small deviations from the background. The practicality of the framework is highlighted, and in addition to its limitations, strategies to simplify complex background modeling are discussed.