The saturation of QCD chiral sum rules of the Weinberg-type is analyzed using ALEPH and OPAL experimental data on the difference between vector and axial-vector correlators (V–A). The sum rules exhibit poor saturation up to current energies below the tau-lepton mass. A remarkable improvement is achieved by introducing integral kernels that vanish at the upper limit of integration. The method is used to determine the value of the finite remainder of the V–A correlator, and its first derivative, at zero momentum: Π(¯ 0) = −4L¯ 10 = 0.0257 ± 0.0003, and Π¯ (0) = 0.065 ± 0.007 GeV−2. The dimension d = 6 and d = 8 vacuum condensates in the operator product expansion are also determined: O6=−(0.004 ± 0.001) GeV6, and O8=−(0.001 ± 0.006) GeV8.

Reference:

Dominguez, C. A., and K. Schilcher. "Finite energy chiral sum rules in QCD." Physics Letters B 581, no. 3 (2004): 193-198.

Dominguez, C. A., & Schilcher, K. (2004). Finite energy chiral sum rules in QCD. Physics Letters B, http://hdl.handle.net/11427/26775

Dominguez, C A, and K Schilcher "Finite energy chiral sum rules in QCD." Physics Letters B (2004) http://hdl.handle.net/11427/26775

Dominguez CA, Schilcher K. Finite energy chiral sum rules in QCD. Physics Letters B. 2004; http://hdl.handle.net/11427/26775.