Transparent expression of theA2condensate’s renormalization

We give a more transparent understanding of the vacuum expectation value of the renormalized local operator $A^2$ by relating it to the gluon propagator integrated over the momentum. The quadratically divergent perturbative contribution is subtracted and the remainder, dominantly due to the ${O(1/p}^2)$ correction to the perturbative propagator at large $p^2$ is logarithmically divergent. This provides a transparent derivation of the fact that this ${O(1/p}^2)$ term is related to the vacuum expectation value of the local $A^2$ operator and confirms a previous claim based on the operator product expansion (OPE) of the gluon propagator. At leading logarithms the agreement is quantitative, with a standard running factor, between the local $A^2$ condensate renormalized as described above and the one renormalized in the OPE context. This result supports the claim that the BRST invariant Landau-gauge $A^2$ condensate might play an important role in describing the QCD vacuum.