the most early work, having used similar methods, see also [@vs; @GRT]) and hadrons, containing two heavy quarks [@DHD1; @DHD2]. As was already pointed in [@DHD1], the expansion, applied here, is simultaneously in the powers of both inverse heavy quark masses and the relative velocity of heavy quarks inside the hadron. Thus, this fact shows the difference between the description for the doubly heavy baryons and the consideration of both the heavy-light mesons (the expansion in powers of $\frac{\Lambda_{QCD}}{m_Q}$) and the heavy-heavy mesons [@Beneke] (the expansion in powers of relative velocity of heavy quarks inside the hadron, where one can apply the scaling rules of nonrelativistic QCD [@4]).

The operator product expansion explored has the form: $${\cal T} = \sum_{i=1}^2 C_1(\mu)\bar Q^iQ^i + \frac{1}{m_{Q^i}^2}C_2(\mu)\bar
Q^i g\sigma_{\mu\nu}G^{\mu\nu}Q^i
+ \frac{1}{m_{Q^i}^3}O(1) \label{4}$$

The leading contribution in Eq.(\[4\]) is determined by the operators $\bar
Q^iQ^i$, corresponding to the spectator decay of $Q^i$-quarks. The use of motion equation for the heavy quark fields allows one to eliminate some redundant operators, so that no operators of dimension four contribute. There is a single operator of dimension five, $Q^i_{GQ} = \bar Q^i g \sigma_{\mu\nu}
G^{\mu\nu} Q^i$. As we will show below, significant contributions come from the operators 