Effect of continuum states on the double-heavy hadron spectra

We present the leading order coupling of double-heavy hadrons to heavy hadron pairs in Born-Oppenheimer effective field theory. We obtain the expressions for the contribution of heavy hadron pairs to the masses and widths of double-heavy hadrons. We apply our result for the specific case of the coupling of the lowest lying heavy hybrids and $D_{\left(s\right)}^{\left(\ast \right)}{\overline{D}}_{\left(s\right)}^{\left(\ast \right)}\left(B_{\left(s\right)}^{\left(\ast \right)}{\overline{B}}_{\left(s\right)}^{\left(\ast \right)}\right)$ \( {D}_{(s)}^{\left(\ast \right)}{\overline{D}}_{(s)}^{\left(\ast \right)}\left({B}_{(s)}^{\left(\ast \right)}{\overline{B}}_{(s)}^{\left(\ast \right)}\right) \) obtaining a set of selection rules for the decays. We build a model for the coupling potential and compute the corresponding decay widths and the contributions to the mass of the heavy hybrids. We compare our results with the experimental exotic quarkonium spectrum and discuss the most likely experimental candidates for quarkonium hybrids.