Towards a determination of the chiral couplings at NLO in 1/N-C: L-8(r)(mu) and Cr-38(r)(mu)

We present a dispersive method which allows to investigate the low-energy couplings of chiral perturbation theory at the next-to-leading order (NLO) in the 1/N-C expansion, keeping full control of their renormalization scale dependence. Using the resonance chiral theory Lagrangian, we perform a NLO calculation of the scalar and pseudoscalar two-point functions, within the single-resonance approximation. Imposing the correct QCD short-distance constraints, one determines their difference II(t) equivalent to IIS(t)-IIP(t) in terms of the pion decay constant and resonance masses. Its low momentum expansion fixes then the low-energy chiral couplings L-8 and C-38. At mu(0) = 0.77 GeV, we obtain L-8(r)(mu(0))(SU(3)) = (0.6 +/- 0.4) (.) 10(-3) and C-38(r)(mu(0))(SU(3)) = (2 +/- 6) (.) 10(-6)