Isospin-breaking effects of the double-charm molecular pentaquarks

Abstract

We investigate isospin-breaking effects in double-charm molecular pentaquarks with the $D^{(*)}Σ_c^{(*)}$ configuration, using the one-boson-exchange potential framework. In these systems, the isospin-breaking effects arise from two sources: the strong interaction, which manifests as the threshold difference of the $D^{(*)}Σ_c^{(*)}$ components in the same isospin multiplet and the mass splittings of the exchanged isovector mesons ($π$ and $ρ$); and the electromagnetic interaction between charged $D^{(*)}$ and $Σ_c^{(*)}$ components. We calculate the binding properties and the isospin mixing angle between the $I=1/2$ and $I=3/2$ states of the $D^{(*)}Σ_c^{(*)}$ system. Our results show that the isospin-breaking effect contributes a significant correction of roughly $10\%-30\%$ to the binding energy. This effect is particularly pronounced in loosely bound molecular candidates, which are characterized by small binding energies and large root-mean-square radii. We therefore conclude that the explicit inclusion of isospin-breaking effects is essential for achieving the precision in theoretical calculations necessary to match rapidly advancing experimental programs. Our results are expected to provide valuable guidance for future high-precision experimental studies of deuteron-like molecular states.

Figures (3)

• Figure 1: A schematic picture of the multiquark states, compact multiquarks (left panel) versus hadronic molecules (right panel) formed by the colorless hadrons.
• Figure 2: Tree-level Feynman diagrams for the four scattering processes $D^{(*)}\Sigma_c^{(*)} \to D^{(*)}\Sigma_c^{(*)}$.
• Figure 3: (Color online) Coulomb interaction between two charged point-like particles and the ones between charged hadrons calculated using Eq. (\ref{['CL4']}). For the latter, three cutoff values are adopted as $a = 1.0\Lambda,~ 2.0\Lambda, ~4.0\Lambda$, with $\Lambda=1.25$ GeV.