Masses and widths of the exotic molecular $B_{(s)}^{(*)} B_{(s)}^{(*)}$ states

Abstract: We study the interaction of the doubly bottom systems $BB$, $B^* B$, $B_s B$, $B_s^* B$, $B^* B^*$, $B^* B_s$, $B^B_s^$, $B_s B_s$, $B_s B_s^*$, $B_s^* B_s^*$ by means of vector meson exchange with Lagrangians from an extension of the local hidden gauge approach. The full s-wave scattering matrix is obtained implementing unitarity in coupled channels by means of the Bethe-Salpeter equation. We find poles below the channel thresholds for the attractively interacting channels $B^* B$ in $I=0$, $B^*_s B-B^*B_s$ in $I=\frac{1}{2}$, $B^* B^*$ in $I=0$, and $B^*_s B^*$ in $I=\frac{1}{2}$, all of them with $J^P=1^+$. For these cases the widths are evaluated identifyng the dominant source of imaginary part. We find binding energies of the order of $10-20$ MeV, and the widths vary much from one system to the other: of the order of 10-100 eV for the $B^* B$ system and $B^*_s B-B^*B_s$, about $6$ MeV for the $B^* B^*$ system and of the order of $0.5$ MeV for the $B^*_s B^*$ system.