Existence of isospin-three-halves Sigma-c D-bar-star molecules

Determine whether the isospin-/2 a3c05D* systems support very shallow bound states with quantum numbers IJ^P = /2/201/201 and /2/201/201, whose existence depends sensitively on the strength of the c3-meson-exchange interaction.

Background

The semirelativistic potential model predicts two nearly degenerate, extremely shallow a3c05D* states in the isospin-/2 sector, lying only approximately 200300 keV below threshold. Their binding is attributed to weak c3 exchange, so changes in the poorly constrained interaction strength could remove the bound states altogether. Consequently, whether these states exist is left unresolved and would require experimental investigation through their predicted narrow decay channels.

References

In another word, the existence of the $\Sigma_c\bar{D}*$ bound states with $IJP=\frac{3}{2}\frac{1}{2}-$ and $\frac{3}{2}\frac{3}{2}-$ highly depend on the strength of the interaction from $\sigma$ exchange. If they exist, they may very narrow states due to their very weak couplings to the main fall-apart channels, such as $\eta_c\Delta$ and $J/\psi \Delta$.

— Hidden charm pentaquarks and the nature of $P_{c}$ states observed at LHCb  (2609.19749 - Liang et al., 17 Sep 2026) in Section 3, subsection 24\Sigma_c\bar{D}^*24 system and 24P_c(4440,4457)24