factor $k^{-\frac{4}{9}}$ accounts for the low energy logarithmic renormalization of $f_D$ constant. We have used this equation for all doubly heavy baryons, considered in this paper. Even though we use this relation to compute central values of lifetimes, the precise values of wavefunction parameters are under question, so in the presented results we have allowed for variations.

The renormalization scale $\mu$ is chosen in the following way: $\mu_1 = m_b$ and $\mu_2 = m_c$ in the estimates of Wilson coefficients $C_{+}(\mu)$ and $C_{-}(\mu)$ for the effective four-fermion weak lagrangian at low energies with the $b$ and $c$-quarks, correspondingly. For nonspectator effects, which are the Pauli interference and weak scattering of valence quarks, the renormalization scale $\mu$ is obtained from the fit of theoretical predictions for the lifetime differences of baryons $\Lambda_c$, $\Xi_c^{+}$ and $\Xi_c^{0}$ over the experimental data.

In Table \[cc\] we present the results of calculations for the doubly charmed baryons. Together with the total lifetimes of these baryons we have shown the relative spectator and nonspectator contributions.

                              $\Xi_{cc}^{++}$   $\Xi_{cc}^{+}$   $\Omega_{cc}^{+}$
  -------------------------- ----------------- ---------------- -------------------
   $\sum c\to s$, ps$^{-1}$        3.104            3.104              3.104
        PI, ps$^{-1}$             -0.874              -                0.621
        WS, ps$^{-1}$                -              1.776                -
          $\tau$, ps               0.45              0.20              0.27

  : The 