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

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 ${\Lambda }_c(2595{)}^{+}$.

Comments: 22 pages, 6 figures. To match the published version in Phys.Rev.D