Heavy meson thresholds in Born-Oppenheimer effective field theory

We consider heavy meson-antimeson pairs and their coupling to quarkonium in the context of nonrelativistic effective field theories (EFTs) incorporating adiabatic expansion. work out all leading order couplings obtain contributions masses widths quarkonia. match new potentials terms QCD. Using available lattice data for coupled system lowest lying pair, we extract mixing potential use it compute numerically $D\overline{D}(B\overline{B})$ ${D}_{s}{\overline{D}}_{s}({B}_{s}{\overline{B}}_{s})$ charmonium (bottomonium) states $l=0$, 1, 2 up $n=6$ covering threshold region. When a state pair are separated by small energy gaps, interactions can be described EFT with contact interactions. matching between two EFTs obtaining wave functions.