Towards a determination of the chiral couplings at NLO in 1/NC: L8r(μ) and C38r(μ)

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/NC expansion, keeping full control of their renormalization scale dependence. Using the res- onance chiral theory Lagrangian, we perform a NLO calculation of the scalar and pseu- doscalar two-point functions, within the single-resonance approximation. Imposing the cor- rect QCD short-distance constraints, one determines their difference |(t) ´ |S(t)i|P(t) in terms of the pion decay constant and resonance masses. Its low momentum expan- sion fixes then the low-energy chiral couplings L8 and C38. At µ0 = 0.77GeV, we obtain L r (µ0) SU(3) = (0.6 ± 0.4) · 10 i3 and C r (µ0) SU(3) = (2 ± 6) · 10 i6 .