of dimension six $Q_{2Q^i2q} = \bar Q^i\Gamma q\bar q\Gamma^{'}Q^i$, representing the effects of Pauli interference and weak scattering for doubly heavy baryons. Furthermore, there are also other operators of dimension six $Q_{61Q^i} = \bar Q^i \sigma_{\mu\nu}\gamma_{l} D^{\mu}G^{\nu l}Q^i$ and $Q_{62Q^i} = \bar Q^i D_{\mu} G^{\mu\nu}\Gamma_{\nu}Q^i$, which are suppressed in comparison with $Q_{2Q^i2q}$ [@vs]. In what follows, we do not calculate the corresponding coefficient functions for the latter two operators, so that the expansion is certainly complete up to the second order of $\frac {1}{m}$, only.

Further, the different contributions to OPE are given by the following: $$\begin{aligned}
{\cal T}_{\Xi_{cc}^{++}} &=& 2 {\cal T}_{35c} + {\cal
T}_{6,PI}^{(1)},\nonumber\\ {\cal T}_{\Xi_{cc}^{+}} &=& 2 {\cal
T}_{35c} + {\cal T}_{6,WS}^{(2)},\nonumber\\ {\cal
T}_{\Omega_{cc}^{+}} &=& 2 {\cal T}_{35c} + {\cal
T}_{6,PI}^{(3)},\nonumber\\ {\cal T}_{\Xi_{bc}^{+}} &=& {\cal
T}_{35b} + {\cal T}_{35c} + {\cal T}_{6,PI}^{(4)} + {\cal
T}_{6,WS}^{(4)},\nonumber\\ {\cal T}_{\Xi_{bc}^{0}} &=& {\cal
T}_{35b} + {\cal T}_{35c} + {\cal T}_{6,PI}^{(5)} + {\cal
T}_{6,WS}^{(5)},\nonumber \\ {\cal T}_{\Omega_{bc}^{0}} &=& {\cal
T}_{35b} + {\cal T}_{35c} + {\cal T}_{6,PI}^{(6)} + {\cal
T}_{6,WS}^{(6)},\nonumber \\ {\cal T}_{\Xi_{bb}^{0}} &=& 2 {\cal
T}_{35b} + {\cal T}_{6,WS}^{(7)},\nonumber\\ {\cal
T}_{\Xi_{bb}^{-}} &=& 2 {\cal T}_{35b} + {\cal
T}_{6,PI}^{(8)},\nonumber \\ {\cal T}_{\Omega_{bb}^{-}} &=& 2
{\cal T}_{35b} + {\cal T}_{6,PI}^{(9)},\nonumber\end{aligned}$$ where the $35$-labelled terms 