Abstract.
Starting from the study of the low-energy and high-energy behaviors of the QCD three-point functions \(\langle V \! A P\rangle\), \(\langle V V \! P\rangle \) and \(\langle A A P\rangle\), several \({\mathcal{O}}(p^6)\) low-energy constants of the chiral Lagrangian are evaluated within the framework of the lowest meson dominance (LMD) approximation to the large-\(N_C\) limit of QCD. In certain cases, values that differ substantially from estimates based on a resonance Lagrangian are obtained. It is pointed out that the differences arise through the fact that QCD short-distance constraints are in general not correctly taken into account in the approaches using resonance Lagrangians. We discuss the implications of our results for the \({\mathcal{O}}(p^6)\) counterterm contributions to the vector form factor of the pion and to the decay \(\pi\to e \nu_e \gamma\), and for the pion–photon–photon transition form factor.
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Received: 4 June 2001 / Published online: 31 August 2001
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Knecht, M., Nyffeler, A. Resonance estimates of \(\mathcal{O}(p^6)\) low-energy constants and QCD short-distance constraints. Eur. Phys. J. C 21, 659–678 (2001). https://doi.org/10.1007/s100520100755
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DOI: https://doi.org/10.1007/s100520100755