# The $\chi_{cJ}$ decay to $\phi K^* \bar K, \phi h_1(1380)$ testing the nature of axial vector meson resonances

## TL;DR

This paper investigates the decay processes of $oldsymbol{ ext{chi}_{cJ}}$ mesons into $oldsymbol{ ext{phi} ext{K}^* ar{ ext{K}}}$ and $oldsymbol{ ext{phi} ext{h}_1(1380)}$, demonstrating how rescattering explains the formation of axial vector mesons and specific interference effects.

## Contribution

It provides a theoretical model showing how the $ ext{h}_1(1380)$ resonance emerges from rescattering in $ ext{chi}_{cJ}$ decays, clarifying the nature of axial vector mesons.

## Key findings

- Explains the absence of $h_1(1380)$ in $ ext{chi}_{c0}$ decay.
- Predicts a dip in the $K^+ ext{pi}^0 K^-$ mass distribution for $ ext{chi}_{c1,2}$ decays.
- Supports the resonance's dynamical generation from vector-pseudoscalar rescattering.

## Abstract

We perform a theoretical study of the $\chi_{cJ} \to \phi K^* \bar K \to \phi K\pi \bar K$ reaction taking into account the $K^* \bar K$ final state interaction, which in the chiral unitary approach is responsible, together with its coupled channels, for the formation of the low lying axial vector mesons, in this case the $h_1(1380)$ given the selection of quantum numbers. Based on this picture we can easily explain why in the $\chi_{c0}$ decay the $h_1(1380)$ resonance is not produced, and, in the case of $\chi_{c1}$ and $\chi_{c2}$ decay, why a dip in the $K^+ \pi^0 K^-$ mass distribution appears in the 1550-1600 MeV region, that in our picture comes from a destructive interference between the tree level mechanism and the rescattering that generates the $h_1(1380)$ state. Such a dip is not reproduced in pictures where the nominal $h_1(1380)$ signal is added incoherently to a background, which provides support to the picture where the resonance appears from rescattering of vector-pseudoscalar components.