States of $\rho D^{\ast }{\bar{D}}^{\ast }$ with $J=3$ within the Fixed Center Approximation to the Faddeev equations

Abstract

We study the interaction of the a $\rho$ and $D^{\ast }$, ${\bar{D}}^{\ast }$ with spins aligned using the Fixed Center Approximation to the Faddeev equations. We select a cluster of $D^{\ast }{\bar{D}}^{\ast }$, which is found to be bound in $I=0$ and can be associated to the X(3915), and let the $\rho$ meson orbit around the $D^{\ast }$ and ${\bar{D}}^{\ast }$. In this case we find an $I=1$ state with mass around 4340 MeV and narrow width of about 50 MeV. We also investigate the case with a cluster of $\rho D^{\ast }$ and let the ${\bar{D}}^{\ast }$ orbit around the system of the two states. The $\rho D^{\ast }$ cluster is also found to bind and leads to the $D_2^{\ast }(2460)$ state. The addition of the extra ${\bar{D}}^{\ast }$ produces further binding and we find, with admitted uncertainties, a state of $I=0$ around 4000 MeV, and a less bound narrow state with $I=1$ around 4200 MeV.

Comments: 12 pages, 5 figures