ProbingCPviolation systematically in differential distributions

We revisit the topic of triple-product asymmetries which probe $CP$ violation through differential distributions. We construct distributions with well-defined discrete symmetry properties and characterize the asymmetries formed upon them. It is stressed that the simplest asymmetries may not be optimal. We explore systematic generalizations having limited reliance on the process dynamics and phase-space parametrization. They exploit larger fractions of the information contained in differential distributions and may lead to increased sensitivities to $CP$ violation. Our detailed treatment of the case of spinless four-body decays paves the way for further experimental studies.