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

Abstract

Starting from the study of the low-energy and high-energy behaviours of the QCD three-point functions VAP , V VP and AAP , several 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 O(p 6 ) counterterm contributions to the vector form factor of the pion and to the decay π → eν e γ, and for the pion-photon-photon transition form factor.

From Hadronic τ Decays to the Chiral Couplings and

“…Our determinations of L r 10 (M ρ ) and C r 87 (M ρ ) agree within errors with the large-N C estimates based on lowest-meson dominance [24,29,37,42],…”

“…There has been a lot of recent activity to determine the chiral LECs from theory, using as much as possible QCD information [23][24][25][26][27][28][29][30][31][32]. This strong effort is motivated by the precision required in present phenomenological applications, which makes necessary to include corrections of O(p 6 ) where the huge number of unknown couplings are the major source of theoretical uncertainty.…”

Decayπ0→γγto next to leading order in chiral perturbation theory

“…has vanishing β-function and its value can be estimated by means of a QCD sum rule for the general three-point function involving the pseudoscalar density and two vector currents and saturating the spectral function in the hadronic sector with the states indicated in Fig. (2), yielding [12,19]:…”

Quantum Loops in the Resonance Chiral Theory: The Vector Form-Factor

“…A useful generalization is the Minimal Hadronic Ansatz, which keeps the minimum number of resonances compatible with all known short-distance constraints for the problem at hand [15]. The resonance contributions to some O(p 6 ) χPT couplings have been already analyzed in this way, by studying an appropriate set of three-point functions [16][17][18]. The N C → ∞ limit of the resonance chiral theory (RχT) has been investigated in many works [8,9,11,[13][14][15][16][17][18] and a very successful leading order phenomenology already exists [11].…”