In this article, we study the ground states and the first radial excited states of the flavor antitriplet heavy baryon states and with the spin-parity by carrying out operator product expansion up to vacuum condensates of dimension in a consistent way. We observe for the first time that the higher dimensional vacuum condensates play an important role, and obtain very stable QCD sum rules with variations of the Borel parameters for the heavy baryon states. The predicted masses , , and for the first radial excited states , , and , respectively, are in excellent agreement with the experimental data and support assigning , , and to be the first radial excited states of , , and , respectively. The predicted mass for can be confirmed using experimental data in the future.