Bound states of charmed baryons and antibaryons

Within the framework of nonrelativistic potential models, we investigate the possibility that bound states of the type ${\overline{B}}_c{B}_c$ may exist, where $B_c$ is a charmed member of the 20 baryon multiplet of SU(4). By rather general considerations, we establish the approximate level order of the bound-state spectrum. Specific potential models are then invoked to qualitatively estimate the binding energies and rms radii of ${\overline{B}}_c{B}_c$ bound states. For reasonably small binding energies ($<~\frac{1}{2}$ GeV), for which a potential description is sensible, such configurations are found to be "quasimolecular" in nature, i.e., having rms radii considerably larger (≥0.7 fm) than the corresponding $\overline{c}c$ quark-model states. We show that most of the low-lying states are isospin $I=0\mathrm{}$ as in the $\overline{c}c$ model. However, because of the coherent effect of tensor forces, certain $I=1\mathrm{}$ configurations of the ${\overline{C}}_1{C}_1$ system experience a downward energy shift, and hence could appear in the same energy region as $I=0\mathrm{}$ states (e.g., ${}_{}{}^{2I+1,2S+1}{}_{}{}^{}L_J^{}{}_{}{}^{}={}_{}{}^{33}{}_{}{}^{}P_0^{}{}_{}{}^{}$ state near ${}_{}{}^{13}{}_{}{}^{}P_{0,1,2}^{}{}_{}{}^{}$ states). The states we describe can mix with and modify the properties of $\overline{c}c$ quark states of the same quantum numbers in the $\frac{J}{\psi },\chi ,{\psi }^{\prime }$ region from 3.1 to 3.7 GeV. Some of them could appear independently as narrow states in the mass region of 4 GeV. "Exotic" ${\overline{C}}_1{C}_1$ states with $I=2\mathrm{}$ are shown to always lie above $I=0,1\mathrm{}$ configurations of the same $L$; however, for a wide class of potential models, the $P$- wave ${\overline{C}}_1{C}_1$ states (${}_{}{}^{53}{}_{}{}^{}P_{0,1,2}^{}{}_{}{}^{},{}_{}{}^{51}{}_{}{}^{}P_1^{}{}_{}{}^{}$) are still bound close to threshold (∼4.8 GeV). We exhibit qualitative arguments that some of these ${\overline{B}}_c{B}_c$ bound states may be narrow. We discuss possible experimental means for finding the $I=1\mathrm{} \mathrm{and} 2$ states, i.e., those not predicted by the $c\overline{c}$ quark model.