QCD sum rules for the nucleon are considered in complex $q^2$ plane with inclusion of the radiative corrections of the order ${\alpha }_s$. It is shown that the radiative corrections affect mainly the residue ${\lambda }^2$ of the nucleon pole. Their influence on the value of the nucleon mass is much smaller. Following the ideas of Ioffe and Zyablyuk we expand the analysis to complex values of $q^2$. This provides a more stable solution. Varying the weights of the contributions of different dimensions by changing the value of the angle in the complex plane we find the value of the six-quark condensate which insures the best consistency of the right hand sides and left-hand sides of the sum rules. The corresponding value of the six-quark condensate appears to be only about $10\%$ smaller then the one, provided by the factorization approximation. The value of the four-quark condensate also appears to be close to the one, corresponding to the factorization assumption. The role of the gluon condensate and its possible values are discussed.

• Received 6 September 2005

DOI:https://doi.org/10.1103/PhysRevD.72.114015