Box singularity conditions in box diagrams of decay processes

A bstract Since 1959, singularities in single-loop diagrams have been a subject of extensive study, as they are believed to play a crucial role in shaping our understanding of experimental observables. In this work, we investigate the singularities arising from box diagrams in decay processes, which can be categorized into two distinct types. We present a comprehensive analysis of these box singularities, deriving explicit conditional expressions that determine their occurrence and discussing the corresponding physical scenarios.