QCD sum rules study of $QQ-\bar{u}\bar{d}$ mesons

We use QCD sum rules to study the possible existence of $QQ-\bar{u}\bar{d}$ mesons, assumed to be a state with $J^{P}=1^{+}$. For definiteness, we work with a current with an axial heavy diquark and a scalar light antidiquark, at leading order in $\alpha_s$. We consider the contributions of condensates up to dimension eight. For the $b$-quark, we predict $M_{T_{bb}}= (10.2\pm 0.3) {\rm GeV}$, which is below the $\bar{B}\bar{B}^*$ threshold. For the $c$-quark, we predict $M_{T_{cc}}= (4.0\pm 0.2) {\rm GeV}$, in agreement with quark model predictions.