the strange quark mass effects in $b$ decays.

The expressions for the contribution of operator $\sum_{i=1}^2O_{GQ^i}$ are known in the leading logarithmic approximation. The expressions for the contributions of operators with the dimension 6 have been calculated by us with account of masses in the final states together with the logarithmic renormalization of the effective lagrangian for the non-relativistic heavy quarks at energies less than the heavy quark masses.

Thus, the calculation of lifetimes for the baryons $\Xi_{QQ'}^{\diamond}$ is reduced to the problem of evaluating the matrix elements of operators, which is the subject of next section.

Matrix elements in NRQCD approximation.
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By using the equations of motion, the matrix element of operator $\bar Q^jQ^j$ can be expanded in series over the powers of ${1}/{m_{Q^j}}$: $$\begin{aligned}
\langle \Xi_{QQ'}^{\diamond}|\bar
Q^jQ^j|\Xi_{QQ'}^{\diamond}\rangle _{norm} = 1 - \frac{\langle
\Xi_{QQ'}^{\diamond}|\bar
Q^j[(i\boldsymbol{D})^2-(\frac{i}{2}\sigma
G)]Q^j|\Xi_{QQ'}^{\diamond}\rangle_{norm}}{2m_{Q^j}^2} +
O(\frac{1}{m_{Q^j}^3}).\end{aligned}$$ Thus, we have to estimate the matrix elements of operators from the following list only: $$\begin{aligned}
&& \bar Q^j(i\boldsymbol{ D})^2Q^j,\quad (\frac{i}{2})\bar
Q^j\sigma GQ^j,\quad \bar Q^j\gamma_{\alpha}(1-\gamma_5)Q^j\bar
q\gamma^{\alpha}(1-\gamma_5)q,\nonumber\\ && \bar
Q^j\gamma_{\alpha}\gamma_5Q^j\bar
q\gamma^{\alpha}(1-\gamma_5)q,\quad \bar
Q^j\gamma_{\alpha}\gamma_5Q^j\bar
Q^k\gamma^{\alpha}(1-\gamma_5)Q^k,\\ && \bar
Q^j\gamma_{\alpha}(1-\gamma_5)Q^j\bar
Q^k\gamma^{\alpha}(1-\gamma_5)Q^k.\nonumber\end{aligned}$$ The meaning of each term in the above list, was already discussed by us in the previous papers on the decays of doubly 