We have calculated the potentials of the heavy (charmed or bottomed) pseudoscalar mesons up to $O(\epsilon^2)$ with the heavy meson chiral perturbation theory. We take into account the contributions from the football, triangle, box, and crossed diagrams with the 2$\phi$ exchange and one-loop corrections to the contact terms. We notice that the total 2$\phi$-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.
Categories: hep-ph hep-ex hep-lat nucl-th