Investigations of the D-multi-rho interactions

In the present work, which aims at searching for bound sates, the interactions of the $D$-multi-$\rho$ systems are investigated by means of the formalism of the fixed-center-approximation to Faddeev equations. Reproducing the states of $f_2 (1270)$ and $D_1 (2420)$ dynamically in the two-body $\rho\rho$ and $\rho D$ interactions, respectively, as the clusters of the fixed center approximation, the state of $D(3000)^0$ is found as a molecule of $D-f_2$ or $\rho-D_1$ structures in the three-body interactions, where we determine its quantum number $J^P = 2^-$ and find another possible state of $D_2 (3100)$ with isospin $I=3/2$. In our results, there are some other predictions with uncertainties, a $D_3 (3160)$ state with $I(J^P) = \frac{1}{2} (3^+)$ in the four-body interactions, a narrow $D_4 (3730)$ state with $I(J^P) = \frac{1}{2} (4^-)$, a wide $D_4 (3410)$ state of $I(J^P) = \frac{1}{2} (4^-)$, and another wide $D_4 (3770)$ state but with $I(J^P) = \frac{3}{2} (4^-)$ in the five-body interactions, and a $D_5 (3570)$ state with $I(J^P) = \frac{1}{2} (5^+)$ in the six-body interactions. Our results are consistent with the findings of quark models.