QCD Sum Rules for Heavy Baryons at Next-to-Leading Order in alpha_s

We derive QCD sum rules for heavy baryons at leading order in $1/m_Q$ and at next-to-leading order in $\alpha_s$. The calculation involves the evaluation of four different perturbative three-loop diagrams which determine the $\alpha_s$-corrections to the Wilson coefficients of the leading term in the Operator Product Expansion (OPE). From the sum rules we obtain estimates for the masses and the residues of the heavy baryons $\Lambda_Q$ and $\Sigma_Q$. The perturbative $O(\alpha_s)$ corrections to the leading order spectral function amount to about $100$, and they shift the calculated values for the baryon masses slightly upward. The residues are shifted upward by about $20-50$. For the bound state energy $\bar\Lambda$ given by the difference of the heavy baryon mass and the pole mass of the heavy quark $m_Q$ we obtain $m_{\Lambda_Q}-m_Q=780 MeV$ and $m_{\Sigma_Q}-m_Q=950 MeV$. For the residues we find $|F_\Lambda|=0.028 GeV^3$ and $|F_\Sigma|=0.039 GeV^3$.