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

Abstract

In this work we study the $\rho B^{\ast }{\bar{B}}^{\ast }$ three-body system solving the Faddeev equations in the fixed center approximation. We assume the $B^{\ast }{\bar{B}}^{\ast }$ system forming a cluster, and in terms of the two-body $\rho B^{\ast }$ unitarized scattering amplitudes in the local Hidden Gauge approach we find a new $I(J^{PC})=1(3^{--})$ state. The mass of the new state corresponds to a two particle invariant mass of the $\rho B^{\ast }$ system close to the resonant energy of the $B_2^{\ast }(5747)$, indicating that the role of this $J=2$ resonance is important in the dynamical generation of the new state.