Resonance estimates of $\mathcal{O}(p^6)$ low-energy constants and QCD short-distance constraints

M. Knecht; A. Nyffeler

doi:doi:10.1007/s100520100755

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2022 Impact factor 4.4

Particles and Fields

Eur. Phys. J. C 21, 659-678 (2001)
DOI: 10.1007/s100520100755

Resonance estimates of $\mathcal{O}(p^6)$ low-energy constants and QCD short-distance constraints

M. Knecht and A. Nyffeler

Centre de Physique Théorique, CNRS-Luminy, Case 907, 13288 Marseille Cedex 9, France

(Received: 4 June 2001 / Published online: 31 August 2001 -© Springer-Verlag / Società Italiana di Fisica 2001 )

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.