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

Abstract

We study the interaction of the a $\rho$ and $D^*$, $\bar D^*$ with spins aligned using the Fixed Center Approximation to the Faddeev equations. We select a cluster of $D^* \bar D^*$, 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 $D^*$ and $\bar D^*$. 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 $\rho D^*$ and let the $\bar D^*$ orbit around the system of the two states. The $\rho D^*$ cluster is also found to bind and leads to the $D^*_2(2460)$ state. The addition of the extra $\bar D^*$ 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.