Box Singularity Conditions in Box Diagrams of Decay Processes

Since 1959, singularities within single-loop diagrams have been studied. They are believed to significantly influence our understanding of experimental observables. In this study, we explore the singularities that arise from box diagrams in the decay process, which can be classified into two distinct categories. A comprehensive analysis of box singularities has been conducted, wherein we have derived and presented specific conditional formulae to ascertain the occurrence of singularities, along with the related physical scenarios.