Revisiting the vector form factor at next-to-leading order in 1/N(C)

Abstract

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 determines it in terms of $F$, $G_V$, $F_A$ and resonance masses. Its low momentum expansion fixes then the low-energy chiral couplings $L_9$ and $C_{88}-C_{90}$ at NLO, keeping full control of their renormalization scale dependence. At ${\mu }_0=0.77$ GeV, we obtain $L_9^r({\mu }_0)=(7.6\pm 0.6)\cdot 10^{-3}$ and $C_{88}^r({\mu }_0)-C_{90}^r({\mu }_0)=(-4.5\pm 0.5)\cdot 10^{-5}$.

Talk given at the 15th International QCD Conference, 28th June-3d July (2010), Montpellier (France)

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