Beyond the narrow resonance approximation: Decay constant and width of the first pion-excitation state

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 MΠ = 1.15 ± 0.28 GeV, width ΓΠ = < 0.48 GeV, decay constant r ≡ [FΠMΠ2fπmπ2]]2 = 4.7 ± 2.8.