Study of the $B^-\to K^-\eta\eta_c$ decay due to the $D\bar{D}$ bound state

TL;DR

This paper investigates the decay process $B^- o K^- o ext{eta eta}_c$ considering meson interactions and a possible $Dar{D}$ bound state, predicting a peak that future experiments can verify.

Contribution

It introduces a coupled-channel approach to dynamically generate the $Dar{D}$ bound state within the decay analysis, providing a novel way to identify such states.

Findings

A peak around 3720 MeV in the $ ext{eta eta}_c$ invariant mass distribution.

The $Dar{D}$ bound state could be observed through this decay channel.

Future experiments can test the existence of the $Dar{D}$ bound state.

Abstract

We study the $B^- \to K^- \eta \eta_c$ decay by taking into account the $S$-wave contributions from the pseudoscalar meson-pseudoscalar meson interactions within the unitary coupled-channel approach, where the $D\bar{D}$ bound state is dynamically generated. In addition, the contribution from the intermediate resonance $K_0^*(1430)^-$, with $K_0^*(1430)^- \to K^-\eta$, is also considered. Our results show that there is a clear peak around $3720$~MeV in the $\eta \eta_c$ invariant mass distribution, which could be associated with the $D \bar{D}$ bound state. The future precise measurements of the $B^- \to K^- \eta \eta_c$ process at the Belle II and LHCb experiments could be, therefore, used to check the existence of the $D \bar{D}$ bound state, and to deepen our understanding of the hadron-hadron interactions.