Identifying the transverse and longitudinal modes of the $K^{\ast }$ and $K_1$ mesons through their angular dependent decay modes

Observing the mass shifts of chiral partners will provide invaluable insight into the role of chiral symmetry breaking in the generation of hadron masses. Because both the $K^{\ast }$ and $K_1$ mesons have vacuum widths smaller than 100 MeV, they are ideal candidates for realizing mass shift measurements. On the other hand, the different momentum dependence of the longitudinal and transverse modes smear the peak positions. In this work, we analyze the angular dependence of the two-body decays of both the $K^{\ast }$ and $K_1$. It is found that the longitudinal and transverse modes of the $K^{\ast }$ can be isolated by observing the pseudoscalar decay in either the forward or perpendicular directions, respectively. For the $K_1$ decaying into a vector meson and a pseudoscalar meson, one can accomplish the same goal by further observing the polarization of the vector meson through its angular dependence on the two pseudoscalar meson decay.