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

TL;DR

This paper calculates the pion vector form factor at NLO in 1/N(C) using Resonance Chiral Theory, determining key chiral couplings with scale dependence and QCD constraints.

Contribution

It provides a novel NLO calculation of the vector form factor and extracts chiral couplings L9 and C88-C90 with controlled scale dependence.

Findings

L9(μ0) = (7.9 ± 0.4) × 10^{-3}

C88(μ0) - C90(μ0) = (-4.6 ± 0.4) × 10^{-5}

Imposes QCD short-distance constraints to fix amplitudes.

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 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}.