Weak decays of doubly heavy baryons: "decay constants"

Inspired by the recent observation of the $\Xi_{cc}^{++}$ by LHCb collaboration, we explore the "decay constants" of doubly heavy baryons in the framework of QCD sum rules. With the $\Xi_{cc}, \Xi_{bc}, \Xi_{bb}$, and $\Omega_{cc}, \Omega_{bc}, \Omega_{bb}$ baryons interpolated by three-quark operators, we calculate the correlation functions using the operator product expansion and include the contribution from operators up to dimension six. On the hadron side, we consider both contributions from the lowest-lying states with $J^P=1/2^+$ and from negative parity baryons with $J^P=1/2^-$. We find that the results are stable and the contaminations from negative parity baryons are not severe. These results are ingredients for the QCD study of weak decays and other properties of doubly-heavy baryons.