Revisiting the vector form factor at next-to-leading order in 1/NC

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 determines it in terms of F, GV, FA and resonance masses. Its low momentum expansion fixes then the low-energy chiral couplings L9 and C88 −C90 at NLO, keeping full control of their renormalization scale dependence. At μ0 = 0.77 GeV, we obtain Lr9(μ0) = (7.6 ± 0.6) ⋅ 10−3 and Cr88(μ0) −Cr90(μ0) = (−4.5 ± 0.5) ⋅ 10−5.