Resonance saturation in the odd-intrinsic parity sector of low-energy QCD

Abstract

Using the large ${N}_{C}$ approximation we have constructed the most general chiral resonance Lagrangian in the odd-intrinsic parity sector that can generate low-energy chiral constants up to $\mathcal{O}({p}^{6})$. Integrating out the resonance fields these $\mathcal{O}({p}^{6})$ constants are expressed in terms of resonance couplings and masses. The role of ${\ensuremath{\eta}}^{\ensuremath{'}}$ is discussed and its contribution is explicitly factorized. Using the resonance basis we have also calculated two QCD Green functions of currents, $⟨VVP⟩$ and $⟨VAS⟩$, and found, imposing high-energy constraints, additional relations for resonance couplings. We have studied several phenomenological implications based on these correlators which provided, for example, a prediction for the ${\ensuremath{\pi}}^{0}$-pole contribution to the muon $g\ensuremath{-}2$ factor: ${a}_{\ensuremath{\mu}}^{{\ensuremath{\pi}}^{0}}=65.8(1.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$.