The vector form factor at the next-to-leading order in 1/NC: chiral couplings L9(μ) and C88(μ) − C90(μ)

Using the Resonance Chiral Theory Lagrangian, we perform a calculation of the vector form factor of the pion at the next-to-leading order (NLO) in the 1/NC expansion. Imposing the correct QCD short-distance constraints, one fixes the amplitude in terms of the pion decay constant F and resonance masses. Its low momentum expansion determines then the corresponding \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{O}\left( {{p^4}} \right) $\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{O}\left( {{p^6}} \right) $\end{document} low-energy chiral couplings at NLO, keeping control of their renormalization scale dependence. At μ0 = 0.77 GeV, we obtain L9(μ0) = (7.9 ± 0.4) ∙ 10−3 and C88(μ0) − C90(μ0) = (−4.6 ± 0.4) ∙ 10−5 .