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.
Highlights
The Λcð2590ÞΣc system can exchange a pion near the mass-shell
For the baryon-antibaryon case this Coulomb-like force is independent of spin: the Yccð5045Þ baryonia will appear either in the spin S 1⁄4 0 or S 1⁄4 1 configurations with G-parities G 1⁄4 ð−1ÞLþSþ1
For the baryon-baryon case the Coulomb-like force is attractive in the spin S 1⁄4 0 configuration, for which a doubly charmed molecule is expected to form near the threshold
Summary
Owing to the opposite intrinsic parity of the Λcð2590Þ and Σc, the pion is exchanged in S-wave This gives rise to a Coulomb-like force that might be able to bind the system. For the baryon-baryon case the Coulomb-like force is attractive in the spin S 1⁄4 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 Λð1405ÞN, Λð1520ÞΣÃ, Ξð1690ÞΣ, DÃs0ð2317ÞD and DÃs1ð2460ÞDÃ molecules. Besides we find it remarkable that there is the possibility of making relatively concrete predictions for heavy hadron molecules without a strong requirement of guessing the short-range physics or using arbitrary form-factors. Yet we will use these type of assumptions to check the robustness of the results
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