Spin effects induced by kinematic singularity

The study of kinematic singularities in scattering amplitudes has long been a topic of interest, with research on triangle singularities becoming a hot issue in hadron spectroscopy in recent years. On one hand, this is because there has been a long-standing expectation to find experimental evidence for the existence of triangle singularities. On the other hand, the contribution of the triangle singularity mechanism may affect the interpretation of certain hadronic state signals, thus holding particular significance for hadron spectroscopy research. Unlike previous studies that primarily focused on the impact of the triangle singularity mechanism on invariant mass spectra, this paper emphasizes how, in certain processes, the triangle singularity mechanism leads to specific patterns and strong energy dependence in the spin orientation of final-state particles. In fact, this energy dependence of spin orientation reflects the variation in the relative probabilities of final-state particles appearing in different spin states as a function of energy. It is not only related to the energy conditions for triangle singularity production but also to the collinear momentum condition of internal particles and their quantum numbers. Therefore, it differs from the energy dependence corresponding to the invariant mass spectra and carries richer information about the reaction mechanism. The study of the spin effects of the triangle singularity mechanism plays an important role in gaining a more comprehensive understanding of its physical effects and in experimentally verifying its contributions. At the same time, due to the unique dependence of spin observables on kinematic conditions, it can be expected that spin observables hold certain potential for studying more general kinematic singularities, warranting further investigation.