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 identifying 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.

• Received 27 January 2022
• Accepted 28 March 2022

DOI:https://doi.org/10.1103/PhysRevD.105.074017

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Published by the American Physical Society