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

TL;DR

This paper investigates multi-$ ho$ interactions with a focus on $D$-multi-$ ho$ systems, predicting several new bound states and resonances using a fixed-center approximation to Faddeev equations, consistent with quark model results.

Contribution

It introduces a novel application of the fixed-center approximation to study $D$-multi-$ ho$ interactions and predicts multiple new bound states and resonances.

Findings

Predicted $D(3000)^0$ as a $D-f_2$ or $ ho-D_1$ molecule with $J^P=2^-$.

Identified potential states $D_2(3100)$, $D_3(3160)$, $D_4(3410)$, $D_4(3730)$, $D_4(3770)$, and $D_5(3570)$ with specific isospin and parity.

Results align with quark model predictions.

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.