Masses and widths of the exotic molecular <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>B</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>s</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mo>*</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup><mml:msubsup><mml:mi>B</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>s</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mo>*</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup></mml:math> states
L. R. Dai, E. Oset, A. Feijoo, R. Molina, L. Roca, A. Martínez Torres, Kanchan Khemchandani
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 $I=0$, ${B}_{s}^{*}B\ensuremath{-}{B}^{*}{B}_{s}$ 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 ${B}_{s}^{*}B\ensuremath{-}{B}^{*}{B}_{s}$, about 6 MeV for the ${B}^{*}{B}^{*}$ system and of the order of 0.5 MeV for the ${B}_{s}^{*}{B}^{*}$ system.