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

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$ϕ$ exchange and one-loop corrections to the contact terms. We notice that the total 2$ϕ$-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.

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