Disentangling longitudinal and transverse modes of the $\phi$ meson through dilepton and kaon decays

Angular distributions of $\phi$ meson decay amplitudes of $e^{+}{e}^{-}$ and $K^{+}{K}^{-}$ channels are computed using both specific interaction Lagrangians and simple arguments relying on angular momentum conservation. Based on the obtained results, we assess methods to experimentally disentangle the longitudinal and transverse polarization modes of the $\phi$ meson and discuss advantages and disadvantages of employing either the leptonic or hadronic decay modes for this task.