The vector form factor at the next-to-leading order in 1/N(C): chiral couplings L9(mu) and C88(mu) - C90(mu)

Understand

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/N(C) 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 O(p4) and O(p6) low-energy chiral couplings at NLO, keeping control of their renormalization scale dependence.
• At mu0=0.77 GeV, we obtain L9(mu0) = (7.9 \pm 0.4) 10^{-3} and C88(mu0)-C90(mu0)=(-4.6 \pm 0.4) 10^{-5}.