The vertex corrections due to the triangle singularity mechanism in the light axial vector meson couplings to $K^*\bar{K}+c.c.$

TL;DR

This paper investigates how triangle singularities influence the vertex couplings of light axial vector mesons to $K^*ar{K}+c.c.$, highlighting the importance of final state interactions and energy dependence near the threshold.

Contribution

It introduces the role of triangle singularities in modifying axial vector meson couplings, emphasizing the energy dependence and D-wave contributions from pion exchange mechanisms.

Findings

Triangle singularity affects vertex couplings near threshold.

Energy dependence and D-wave amplitudes are introduced.

Final state interactions significantly influence axial vector meson properties.

Abstract

The light axial vector mesons can couple to $K^*\bar{K}+c.c.$ in an $S$ wave at the tree level. Due to the near-threshold $S$-wave interactions the couplings can be affected by the final state interactions. It is of peculiar interest that the pion exchange between $K^*\bar{K}+c.c.$ can go through a triangle diagram which is within the kinematics of the triangle singularity (TS). This mechanism will introduce energy dependence and a $D$-wave amplitude to the vertex couplings. Hence, it should be necessary to investigate the role played by the $K^*\bar{K}+c.c.$ threshold in order to have a better understanding of the light axial vector spectrum.