$D^{(\ast)}N$ interaction and the structure of $\Sigma_c(2800)$ and $\Lambda_c(2940)$ in chiral effective field theory

Abstract

We study the $DN$ and $D^\ast N$ interactions to probe the inner structure of $\Sigma_c(2800)$ and $\Lambda_c(2940)$ with the chiral effective field theory to the next-to-leading order. We consider the contact term, one-pion-exchange and two-pion-exchange contributions to characterize the short-, long- and mid-range interactions of the $D^{(\ast)}N$ systems. The low energy constants of the $D^{(\ast)}N$ systems are related to those of the $N\bar{N}$ interaction with quark level Lagrangian that inspired by the resonance saturation model. The $\Delta(1232)$ degree of freedom is also included in the loop diagrams. The attractive potential in the $[DN]_{J=1/2}^{I=1}$ channel is too weak to form bound state, which indicates the explanation of $\Sigma_c(2800)$ as the compact charmed baryon is more reasonable. Meanwhile, the potentials of the isoscalar channels are deep enough to yield the molecular states. We obtain the masses of the $[DN]_{J=1/2}^{I=0}$, $[D^\ast N]_{J=1/2}^{I=0}$ and $[D^\ast N]_{J=3/2}^{I=0}$ systems to be $2792.0$ MeV, $2943.6$ MeV and $2938.4$ MeV, respectively. The $\Lambda_c(2940)$ is probably the isoscalar $D^\ast N$ molecule considering its low mass puzzle. Besides, the $\Lambda_c(2940)$ signal might contain the spin-$\frac{1}{2}$ and spin-$\frac{3}{2}$ two structures, which can qualitatively explain the significant decay ratio to $D^0p$ and $\Sigma_c\pi$. We also study the $\bar{B}^{(\ast)}N$ systems and predict the possible molecular states in the isoscalar channels. We hope experimentalists could hunt for the open charmed molecular pentaquarks in the $\Lambda_c^+\pi^+\pi^-$ final state.