Probing double hadron resonances by the complex scaling method

TL;DR

This paper extends the complex scaling method to study bound and resonant states of certain hadron systems, finding resonances in some configurations and providing predictions for their energies and widths relevant to experiments.

Contribution

It introduces a novel application of the complex scaling method to hadron systems, specifically analyzing $ ext{Lambda}_c D$, $ ext{Lambda}_c ar D$, and $ ext{Lambda}_c ext{Lambda}_c$ systems, and predicts the existence of observable resonant states.

Findings

No bound or resonant states in $ ext{Lambda}_c D$ system.

Resonant states exist in $ ext{Lambda}_c ar D$ and $ ext{Lambda}_c ext{Lambda}_c$ systems.

P wave resonances are more stable and potentially observable.

Abstract

Many newly discovered excited states are interpreted as bound states of hadrons. Can these hadrons also form resonant states? In this paper, we extend the complex scaling method (CSM) to calculate the bound state and resonant state consistently for the $\Lambda_c D(\bar D)$ and $\Lambda_c \Lambda_c (\bar \Lambda_c)$ systems. For these systems, the $\pi, \eta, \rho$ meson exchange contributions are suppressed, the contributions of intermediate- and short-range forces from $\sigma/\omega$ exchange are dominant. Our results indicate that $\Lambda_c D$ system can not form bound state and resonant state. There exist resonant states in a wide range of parameters for $\Lambda_c \bar D$ and $\Lambda_c \Lambda_c (\bar \Lambda_c)$ systems. For these systems, the larger bound state energy, the easier to form resonant states. Among all the resonant states, the energies and widths of the P wave resonant states are smaller and more stable, which is possible to be observed in the experiments. The energies of D and F wave resonant states can reach dozens of MeV and the widths can reach hundreds of MeV.