Isospin-breaking effects of the double-charm molecular pentaquarks

We investigate isospin-breaking effects in double-charm molecular pentaquarks with the $D^{(*)}\Sigma_c^{(*)}$ 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 $D^{(*)}\Sigma_c^{(*)}$ components in the same isospin multiplet and the mass splittings of the exchanged isovector mesons ($\pi$ and $\rho$); and the electromagnetic interaction between charged $D^{(*)}$ and $\Sigma_c^{(*)}$ components. We calculate the binding properties and the isospin mixing angle between the $I=1/2$ and $I=3/2$ states of the $D^{(*)}\Sigma_c^{(*)}$ 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.