Are there near-threshold Coulomb-like Baryonia?

Abstract

The $\Lambda_c(2590) \Sigma_c$ system can exchange a pion near the mass-shell. Owing to the opposite intrinsic parity of the $\Lambda_c(2590)$ and $\Sigma_c$, the pion is exchanged in S-wave. This gives rise to a Coulomb-like force that might be able to bind the system. If one takes into account that the pion is not exactly on the mass shell, there is a shallow S-wave state, which we generically call the $Y_{cc}(5045)$ and $Y_{c\bar c}(5045)$ for the $\Lambda_c(2590) \Sigma_c$ and $\Lambda_c(2590) \bar{\Sigma}_c$ systems respectively. For the baryon-antibaryon case this Coulomb-like force is independent of spin: the $Y_{c\bar c}(5045)$ baryonia will appear either in the spin $S=0$ or $S=1$ configurations with G-parities $G=(-1)^{L+S+1}$. For the baryon-baryon case the Coulomb-like force is attractive in the spin $S=0$ configuration, for which a doubly charmed molecule is expected to form near the threshold. This type of spectrum might be very well realized in other molecular states composed of two opposite parity hadrons with the same spin and a mass difference close to that of a pseudo-Goldstone boson, of which a few examples include the $\Lambda(1405) N$, $\Lambda(1520) \Sigma^*$, $\Xi(1690) \Sigma$, $D_{s0}^*(2317) D$ and $D_{s1}^*(2460) D^*$ molecules.