applied to the $\Xi_{QQ'}^{(*)}$-baryon total decay width $\Gamma_{\Xi_{QQ'}^{(*)}}$, can be written down as: $$\Gamma_{\Xi_{QQ'}^{(*)}} =
\frac{1}{2M_{\Xi_{QQ'}^{(*)}}}\langle\Xi_{QQ'}^{(*)}|{\cal T}
|\Xi_{QQ'}^{(*)}\rangle ,
\label{1}$$ where the $\Xi_{QQ'}^{(*)}$ state in Eq. (\[1\]) has the ordinary relativistic normalization, $\langle \Xi_{QQ'}^{(*)}|\Xi_{QQ'}^{(*)}\rangle  = 2EV$, and the transition operator ${\cal T}$ is determined by the expression $${\cal T} = \Im m\int d^4x~\{{\hat T}H_{eff}(x)H_{eff}(0)\},$$ where $H_{eff}$ is the standard effective hamiltonian, describing the low energy interactions of initial quarks with the decays products, so that $$H_{eff} = \frac{G_F}{2\sqrt 2}V_{q_3q_4}V_{q_1q_2}^{*}[C_{+}(\mu)O_{+} +
C_{-}(\mu)O_{-}] + h.c.$$ where $$O_{\pm} = [\bar q_{1\alpha}\gamma_{\nu}(1-\gamma_5)q_{2\beta}][\bar
q_{3\gamma}\gamma^{\nu}(1-\gamma_5)q_{4\delta}](\delta_{\alpha\beta}\delta_{
\gamma\delta}\pm\delta_{\alpha\delta}\delta_{\gamma\beta}),$$ and $$C_+ = \left [\frac{\alpha_s(M_W)}{\alpha_s(\mu)}\right ]^{\frac{6}{33-2f}},
\quad
C_- = \left [\frac{\alpha_s(M_W)}{\alpha_s(\mu)}\right ]^{\frac{-12}{33-2f}},\\$$ where f is the number of flavors, $\{\alpha,\beta,\gamma,\delta \}$ run over the color indeces.

Under an assumption, that the energy release in the heavy quark decay is large, we can perform the operator product expansion for the transition operator ${\cal T}$ in Eq.(\[1\]). In this way we obtain series of local operators with increasing dimensions over the energy scale, wherein the contributions to $\Gamma_{\Xi_{QQ'}^{(*)}}$ are suppressed by the increasing inverse powers of the heavy quark masses. This formalism has already been applied to calculate the total decay rates for the hadrons, containing a single heavy quark [@bigi] (for 