States of $ \rho$ B* $ \bar{{B}}^{{*}}_{}$ with J = 3 within the fixed center approximation to Faddeev equations

Abstract

In this work we study the $\rho B^*\bar{B}^*$ three-body system solving the Faddeev equations in the fixed center approximation. We assume the $B^*\bar{B}^*$ system forming a cluster, and in terms of the two-body $\rho B^*$ 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 $B^\ast_2(5747)$, indicating that the role of this $J=2$ resonance is important in the dynamical generation of the new state.