# ${\overline{B}}^{\left(*\right)}{\overline{B}}^{\left(*\right)}$ interactions in chiral effective field theory

Wang, Bo (School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China) (Research Center for Hadron and CSR Physics, Lanzhou University & Institute of Modern Physics of CAS, Lanzhou 730000, China) (School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China) (Center of High Energy Physics, Peking University, Beijing 100871, China) ; Liu, Zhan-Wei (School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China) (Research Center for Hadron and CSR Physics, Lanzhou University & Institute of Modern Physics of CAS, Lanzhou 730000, China) ; Liu, Xiang (School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China) (Research Center for Hadron and CSR Physics, Lanzhou University & Institute of Modern Physics of CAS, Lanzhou 730000, China)

12 February 2019

Abstract: In this work, the intermeson interactions of double-beauty $\overline{B}\overline{B}$, $\overline{B}{\overline{B}}^{*}$, and ${\overline{B}}^{*}{\overline{B}}^{*}$ 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 behaviors 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 $I\left({J}^{P}\right)=0\left({1}^{+}\right)$ $\overline{B}{\overline{B}}^{*}$ and ${\overline{B}}^{*}{\overline{B}}^{*}$ systems are attractive, and the corresponding binding energies in these two channels are solved to be $\Delta {E}_{\overline{B}{\overline{B}}^{*}}\simeq -{12.6}_{-12.9}^{+9.2}\text{}\text{}\mathrm{MeV}$ and $\Delta {E}_{{\overline{B}}^{*}{\overline{B}}^{*}}\simeq -{23.8}_{-21.5}^{+16.3}\text{}\text{}\mathrm{MeV}$, respectively. The masses of $0\left({1}^{+}\right)$ $\overline{B}{\overline{B}}^{*}$ and ${\overline{B}}^{*}{\overline{B}}^{*}$ states lie above the threshold of their electromagnetic decay modes $\overline{B}\overline{B}\gamma$ and $\overline{B}\overline{B}\gamma \gamma$, and thus they can be reconstructed 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.

Published in: Physical Review D 99 (2019)