$\rho$ Meson Decays of Heavy Hybrid Mesons

We calculate the $\rho$ meson couplings between the heavy hybrid doublets H^h/S^h/M^h/T^h and the ordinary q\bar{Q} doublets in the framework of the light-cone QCD sum rule. The sum rules obtained rely mildly on the Borel parameters in their working regions. The resulting coupling constants are rather small in most cases.