Transparent expression of the A 2 condensate’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.