Non-perturbative non-locality: V ±A correlators in euclidean position space

Using an OPE modification, which takes non-perturbative non-locality into account, the difference and sum of vector and axial-vector correlators are evaluated in euclidean position space. For distances up to 0.8 fm the calculated behavior is close to the instanton liquid result and the ALEPH data, in contrast to the implications of the conventional OPE. The determination of the momentum or distance range in which a truncated operator product expansion (OPE) in QCD approximates well is very important for many applications. Based on global quark-hadron duality the low-energy precision measurements of the spectral functions of vector and axial-vector channels (ALEPH experiment τ → ντ+hadrons [1]) could be confronted with the associated OPE’s [2] but also with the instanton liquid model [3] and lattice calculations [4]. In this letter we investigate how OPE-based non-perturbative non-locality affects the behavior of the V ± A correlators in euclidean position space. The results are compared to the instanton liquid data of [3] and the conventional OPE approach. Working in the chiral limit, in which both Π μν are transverse, and applying naive vacuum saturation at dimension 6, we obtain the following truncated OPE’s [3] at a large normalization scale Q0 RV−A(x)|Q0 ≡ Π (x)− Π(x) 2Π0(x) ∣