In the limitmQ>mQvrel>mQvrel2?ΛQCDhadronic states with two heavy quarksQshould be describable by a version of HQET where the heavy quark is replaced by a di-quark degree of freedom. In this limit the di-quark is a small (compared with1/ΛQCD) color anti-triplet, bound primarily by a color Coulomb potential. The excited Coulombic states and color six states are much heavier than the color anti-triplet ground state. The low lying spectrum of hadrons containing two heavy quarks is then determined by the coupling of the light quarks and gluons with momentum of orderΛQCDto this ground state di-quark. In this short paper we calculate the coefficient of leading local operator(Sv?Sv)(qˉγμvμq)that couples this color anti-triplet di-quark fieldSv(with four-velocityv) directly to the light quarksqin the low energy effective theory. It isO(1/(αs(mQvrel)mQ2)). While our work is mostly of pedagogical value we make an estimate of the contribution of this operator to the masses ofΞbbqbaryon andTQQqˉqˉtetraquark using the non-relativistic constituent quark model.
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