$\bar{B}^{(\ast)} \bar{B}^{(\ast)}$ interactions in chiral effective field theory

Abstract

In this work, the intermeson interactions of double-beauty $\bar{B}\bar{B}$, $\bar{B}\bar{B}^\ast$, and $\bar{B}^\ast\bar{B}^\ast$ systems have been studied with heavy meson chiral effective field theory. The effective potentials are calculated with Weinberg's scheme up to one-loop level. At the leading order, four body contact interactions and one pion exchange contributions are considered. In addition to two pion exchange diagrams, we include the one-loop chiral corrections to contact terms and one pion exchange diagrams at the next-to-leading order. The behaviours of effective potentials both in momentum space and coordinate space are investigated and discussed extensively. We notice the contact terms play important roles in determining the characteristics of the total potentials. Only the potentials in $I(J^P)=0(1^+)$ $\bar{B}\bar{B}^\ast$ and $\bar{B}^\ast\bar{B}^\ast$ systems are attractive, and the corresponding binding energies in these two channels are solved to be $\Delta E_{\bar{B}\bar{B}^\ast}\simeq -12.6^{+9.2}_{-12.9}$ MeV and $\Delta E_{\bar{B}^\ast\bar{B}^\ast}\simeq -23.8^{+16.3}_{-21.5}$ MeV, respectively. The masses of $0(1^+)$ $\bar{B}\bar{B}^\ast$ and $\bar{B}^\ast\bar{B}^\ast$ states lie above the threshold of their electromagnetic decay modes $\bar{B}\bar{B}\gamma$ and $\bar{B}\bar{B}\gamma\gamma$, and thus they can be reconstructable via electromagnetic interactions. Our calculation not only provides some useful information to explore exotic doubly-bottomed molecular states for future experiments, but also is helpful for the extrapolations of Lattice QCD simulations.