Resonance on top of thresholds: the $\Lambda_c(2595)^+$ as an extremely fine-tuned state

TL;DR

This study investigates the nature of the $ ext{Lambda}_c(2595)^+$ resonance by analyzing $ ext{pi} ext{Sigma}_c$ scattering near thresholds, revealing the importance of CDD poles and isospin effects, and concluding the resonance is not predominantly a $ ext{pi}^0 ext{Sigma}_c^+$ composite.

Contribution

The paper introduces a novel framework to handle CDD poles near thresholds and extends it to coupled channels, improving the understanding of the $ ext{Lambda}_c(2595)^+$ structure.

Findings

Effective range expansion fails near the pole due to CDD poles.

Finite-width effects are crucial for matching experimental width.

$ ext{pi}^0 ext{Sigma}_c^+$ component is subdominant in $ ext{Lambda}_c(2595)^+$.

Abstract

A dedicated study of the $\pi\Sigma_c$ scattering around its threshold is carried out in this work to probe the nature of $\Lambda_c(2595)^+$. We first demonstrate that the effective range expansion approach fails to work near the $\Lambda_c(2595)^+$ pole position, due to the presence of a nearby CDD pole around the $\pi\Sigma_c$ thresholds. We then develop a general framework to properly handle the situation with a CDD pole accompanied by nearby thresholds, which is first elaborated for the single-channel case and then generalized to the coupled-channel study. The isospin breaking effects of the three $\pi\Sigma_c$ channels with different thresholds are specially taken into account in our study. The finite-width effects from the $\Sigma_c$ baryons are considered and found to be relevant to give the $\Lambda_c(2595)^+$ width fully compatible to its experimental value. Through the compositeness analysis, our robust conclusion is that the $\pi^0\Sigma_c^+$ component is subdominant inside the $\Lambda_c(2595)^+$.