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The full version of QCD light-cone sum rule method is applied to tetraquarkscontaining a single heavy $b$ or $c$ quark. To this end, investigations of thestrong vertices $X_{b}X_{b}\rho$ and $X_{c}X_{c}\rho$ are performed, where$X_b=[su][\bar b\bar d]$ and $X_c=[su][\bar c\bar d]$ are the exotic statesbuilt of four quarks of different flavors. The strong coupling constants$G_{X_{b}X_{b}\rho}$ and $G_{X_{c}X_{c}\rho}$ corresponding to these verticesare found using the $\rho$-meson leading and higher-twist distributionamplitudes. In the calculations $X_{b}$ and $X_{c}$ are treated as scalar boundstates of a diquark and antidiquark.

Application of the QCD light cone sum rule to tetraquarks: the strong vertices $X_bX_b\rho$ and $X_cX_c\rho$