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

Determine whether the isospin-/2 a3c*\u0305D* systems support bound states, whose existence depends strongly on the strength of the c3-exchange potential.

Background

The model finds that possible isospin-/2 a3c*\u0305D* bound states would have binding energies of only about 200300 keV and large root-mean-square radii of roughly 5.2 fm. Because the binding is generated primarily by a weak and uncertain c3-meson exchange, the calculation does not establish that these states exist.

References

In the isospin $I=3/2$ sector, the existence of the $\Sigma_c\bar{D}^$ bound states highly depends on the strength of the $\sigma$ exchange potential. If they exist indeed, they should have very small binding energies of $B.E.\simeq 200-300$ keV and fairly large root-mean-square radii of $\sim 5.2$ fm.

— 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