Mass, width, and decay constant of the first pion-excitation: a QCD sum rule approach

A Laplace QCD sum rule treatment of the first pion excitation (Pi) as a subcontinuum resonance in the pseudoscalar channel is presented. Parameters characterizing this resonance are obtained via a global sum rule fit to the hadronic (pi + Pi + continuum) content of the appropriate sum rule, incorporating I) Breit-Wigner departures from the narrow resonance approximation, 2) explicit direct single-instanton contributions, and 3) purely perturbative field-theoretical contributions to two-and three-loop order. The results of this analysis [M-Pi = 1.15 +/- 0.28 GeV, Gamma(Pi) < 0.48 GeV, r = (FPiMPi4)-M-2/f(pi)(2)m(pi)(4) = 4.7 +/- 2.8; uncertainties are 90% confidence levels] are consistent with the present empirical range of the Pi(1300) mass, and predict a rather large decay constant for this resonance. A by-product of this analysis is the prediction (m(u) + m(d))/2 = 7.7 +/- 2.2 MeV for the light quark masses evaluated at an energy scale of 1 GeV.