Investigations of the $D$-multi-$\rho$ interactions

Abstract

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.

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