"Inevitable'' nonstrange tetraquark states and $ρρ$ interaction

Investigation of the interaction between two $ρ$ mesons with $IJ=00, 02, 11, 20$ and $22$ is conducted systematically in the framework of the quark delocalization color screening model. The results show that there is a strong attractive potential between two $ρ$ mesons, which makes it easier for these two mesons to form bound states. The largest binding energies occur for $IJ=02$ and $IJ=00$ with values over a hundred MeV, while the $IJ=20$ state is the least bound and has a binding energy of only a few MeV. Moreover, the results of intercluster distances favor a molecular interpretation of these states. The interaction analysis reveals that the $ρρ$ and $ΔΔ$ interactions share certain similarities. Drawing inspiration from the $d^*$ dibaryon prediction and from decay-property analyses, we suggest that the $ρρ$ with $IJ=02$ may be the most promising candidate of the ``inevitable'' nonstrange tetraquark state, which deserves experimental search.