Beyond the Narrow Resonance Approximation: Decay Constant and Width of the First Pion-Excitation State

Abstract

We consider the first pion excitation as a sub-continuum resonance in the pseudoscalar channel, and we obtain parameters characterizing this resonance through a global fit of the Borel-parameter dependence of the field-theoretical pseudoscalar Laplace sum rule to its hadronic (pion + pion-excitation + QCD-continuum) content. Our analysis incorporates finite-width deviations from the narrow resonance approximation, instanton effects, and higher-loop perturbative contributions to the pseudoscalar correlator. We obtain the following values (uncertainties reflect 90% confidence levels): mass $M_\Pi = 1.15 \pm 0.28 GeV$, width $\Gamma_\Pi = < 0.48 GeV$, decay constant $r \equiv [F_\Pi M_\Pi^2 / f_\pi m_\pi^2]^2 = 4.7 \pm 2.8$.