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 $M_{\Pi }=1.15\pm 0.28GeV$, width ${\Gamma }_{\Pi }=<0.48GeV$, decay constant $r\equiv [F_{\Pi }{M}_{\Pi }^2/f_{\pi }{m}_{\pi }^2{]}^2=4.7\pm 2.8$.

Comments: 9 pages, revtex, no figures, accepted for publication in Phys. Lett. B