Chiral Perturbation Theory and the $\bar{B}\bar{B}$ Strong Interaction

Abstract

We have calculated the potentials of the heavy (charmed or bottomed) pseudoscalar mesons up to $O({ϵ}^2)$ with the heavy meson chiral perturbation theory. We take into account the contributions from the football, triangle, box, and crossed diagrams with the 2$\varphi$ exchange and one-loop corrections to the contact terms. We notice that the total 2$\varphi$-exchange potential alone is attractive in the small momentum region in the channel ${\bar{B}\bar{B}}^{I=1}$, ${{\bar{B}}_s{\bar{B}}_s}^{I=0}$, or ${\bar{B}{\bar{B}}_s}^{I=1/2}$, while repulsive in the channel ${\bar{B}\bar{B}}^{I=0}$. Hopefully the analytical chiral structures of the potentials may be useful in the extrapolation of the heavy meson interaction from lattice QCD simulation.

Comments: 14 pages, 8 figures, 4 tables; discussion extended, references added, version published in Phys. Rev. D