Finite energy chiral sum rules in QCD

Details Finite energy chiral sum rules in QCD Finite energy chiral sum rules in QCD

2003-09-25

arxiv.org/abs/hep-ph/0309285v2

Phys.Lett. B581 (2004) 193-198

Physics

High Energy Physics

High Energy Physics - Phenomenology

Additional references added. No changes in results/conslusions

Scientific paper

10.1016/j.physletb.2003.11.009

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: $\bar{\Pi}(0) = - 4 \bar{L}_{10} = 0.0257 \pm 0.0003 ,$ and $\bar{\Pi}^{\prime}(0) = 0.065 \pm 0.007 {GeV}^{-2}$. The dimension $d=6$ and $d=8$ vacuum condensates in the Operator Product Expansion are also determined: $<{\cal {O}}_{6}> = -(0.004 \pm 0.001) {GeV}^6,$ and $<{\cal {O}}_{8}> = -(0.001 \pm 0.006) {GeV}^8.$

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