Chiral sum rules and duality in QCD

The ALEPH data on the vector and axial-vector spectral functions, extracted from tau-lepton decays, is used in order to test local and global duality, as well as a set of four QCD chiral sum rules. These are the Das-Mathur-Ok ubo sum rule, the first and second Weinberg sum rules, and a relation for t he electromagnetic pion mass difference. We find these sum rules to be poor ly saturated, even when the upper limit in the dispersion integrals is as h igh as 3 GeV2. Since perturbative QCD, plus condensates, is expected to be valid for \q(2)\ greater than or equal to O(1 GeV2) in the whole complex en ergy plane, except in the vicinity of the right hand cut, we propose a modi fied set of sum rules with weight factors that vanish at the end of the int egration range on the real axis. These sum rules are found to be precocious ly saturated by the data to a remarkable extent. As a byproduct, we extract for the low energy renormalization constant (L) over bar(10) the value -4 (L) over bar(10) = 2.43 x 10(-2), to be compared with the standard value -4 (L) over bar(10) = (2.73 +/- 0.12) x 10(-2). This in rum leads to a pion p olarizability alpha(E) = 3.7 x 10(-4) fm(3). (C) 1999 Published by Elsevier Science B.V. All rights reserved.