Pole analysis for the $D^{*}\bar K$-$D\bar{K^*}$ coupled-channel system

TL;DR

This paper investigates possible hadronic molecules in the coupled $D^*\bar K$-$D\bar K^*$ system using the Lippmann-Schwinger equation with meson exchange potentials, identifying a virtual state and a resonance with specific properties.

Contribution

It introduces a comprehensive analysis of the coupled-channel system considering both vector and pseudoscalar meson exchanges, including three-body dynamics and decay effects.

Findings

Identifies a virtual state at 2487 MeV as a cusp in the invariant mass distribution.

Finds a resonance at 2759 MeV with an 18 MeV width.

Provides insights into the manifestation of these states in experimental observables.

Abstract

By solving the Lippmann-Schwinger equation, possible hadronic molecules in the $D^*\bar K$-$D\bar K^*$ coupled-channel system are investigated with the one-meson exchange potentials, where both vector and pseudoscalar mesons are considered as exchange particles. We find an S-wave virtual state with mass $M=2487$ MeV, and a resonance with $M=2759$ and width $\Gamma=18$ MeV. In the $D^* \bar K$ invariant mass distribution, the virtual state appears as a cusp at the $D^*\bar K$ threshold, while the resonance potentially manifests as a dip. In particular, we take into account the $D\bar K \pi$ three-body dynamics due to the on-shell pion exchange and the finite decay width for $\bar K^*$.