2(m_c+m_s)\cdot |\Psi^{dl}(0)|^2,\\ \langle
\Omega_{bc}|(\bar c\gamma_{\mu}\gamma_5c)(\bar
s\gamma^{\mu}(1-\gamma_5)s)|\Omega_{bc}\rangle  &=& 0,\\
\langle \Xi_{bb}^{\diamond}|(\bar b\gamma_{\mu}(1-\gamma_5)b)(\bar
q\gamma^{\mu}(1-\gamma_5)q)|\Xi_{bb}^{\diamond}\rangle  &=& 12(m_b+m_q)\cdot
|\Psi^{dl}(0)|^2,\\
\langle \Xi_{bb}^{\diamond}|(\bar b\gamma_{\mu}\gamma_5 b)(\bar
q\gamma^{\mu}(1-\gamma_5)q)|\Xi_{bb}^{\diamond}\rangle  &=& 8(m_b+m_q)\cdot
|\Psi^{dl}(0)|^2.\end{aligned}$$ The color structure of wave functions leads to the relations $$\langle \Xi_{QQ'}^{\diamond}|(\bar Q_iT_{\mu}Q_k)(\bar
q_k\gamma^{\mu}(1-\gamma_5)q_i)|\Xi_{QQ'}^{\diamond}\rangle
=
-\langle \Xi_{QQ'}^{\diamond}|(\bar QT_{\mu}Q)(\bar
q\gamma^{\mu}(1-\gamma_5)q)|\Xi_{QQ'}^{\diamond}\rangle ,$$ where $T_{\mu}$ is an arbitrary spinor matrix.

Numerical estimates
===================

Performing the numerical calculations of lifetimes for the doubly heavy baryons, we have used the following set of parameters: $$\begin{aligned}
&&m_s = 0.2~\mbox{GeV}\quad m_l = 0.~GeV\quad m_s^{*} =
0.45~\mbox{GeV}\quad m_l^{*} = 0.3~\mbox{GeV}\nonumber
\label{parameters}\\ &&\quad\quad |V_{cs}| = 0.9745 \quad |V_{bc}|
= 0.04 \quad T = 0.4~\mbox{GeV}
\\ &&\quad\quad\quad m_c = 1.55~\mbox{GeV}\quad m_b = 5.05~\mbox{GeV}\end{aligned}$$ The numerical values of diquark wavefunctions at the origin for baryons under consideration are collected in Table \[WF\]. The masses of doubly heavy baryons may be found in Table \[Bmasses\].

                                       $\Xi_{cc}^{++}$   $\Xi_{cc}^{+}$   $\Omega_{cc}^{+}$   $\Xi_{bc}^{+}$   $\Xi_{bc}^{0}$   $\Omega_{bc}^{0}$   $\Xi_{bb}^{0}$   $\Xi_{bb}^{-}$   $\Omega_{bb}^{-}$
  ----------------------------------- ----------------- ---------------- ------------------- ---------------- ---------------- ------------------- ---------------- ---------------- -------------------
   $\Psi^d (0)$, GeV$^{\frac{3}{2}}$        0.150            0.150              0.150             0.205            0.205              0.205             0.380            0.380              0.380

  : The values of diquark wavefunctions for the doubly heavy baryons at the origin.[]{data-label="WF"}

                  $\Xi_{cc}^{++}$   $\Xi_{cc}^{+}$   $\Omega_{cc}^{+}$   $\Xi_{bc}^{+}$   $\Xi_{bc}^{0}$   $\Omega_{bc}^{0}$   $\Xi_{bb}^{0}$   $\Xi_{bb}^{-}$   $\Omega_{bb}^{-}$
  -------------- ----------------- ---------------- ------------------- ---------------- ---------------- ------------------- ---------------- ---------------- -------------------
     