Masses and widths of the exotic molecular $B_{(s)}^{(\ast )}{B}_{(s)}^{(\ast )}$ states

Abstract

We study the interaction of the doubly bottom systems $BB$, $B^{\ast }B$, $B_{s}B$, $B_s^{\ast }B$, $B^{\ast }{B}^{\ast }$, $B^{\ast }{B}_s$, $B^{\ast }{B}_s^{\ast }$, $B_s{B}_s$, $B_s{B}_s^{\ast }$, $B_s^{\ast }{B}_s^{\ast }$ 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 $B^{\ast }B$ in $I=0$, $B_s^{\ast }B-B^{\ast }{B}_s$ in $I=\frac{1}{2}$, $B^{\ast }{B}^{\ast }$ in $I=0$, and $B_s^{\ast }{B}^{\ast }$ 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 $B^{\ast }B$ system and $B_s^{\ast }B-B^{\ast }{B}_s$, about $6$ MeV for the $B^{\ast }{B}^{\ast }$ system and of the order of $0.5$ MeV for the $B_s^{\ast }{B}^{\ast }$ system.

23 pages, 10 figures