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

By M. Knecht, A. Nyffeler. 2001

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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.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/1691adeac0e500d9ed65ad1936602ebcf7d530b9