QCD sum rules and the II (1300) resonance

Global fits to the shape of the first QCD Laplace sum rule exhibiting sensitivity to pionresonance [ Π (1300) ] parameters are performed, leading to predictions for the pion-resonance mass and decay constant. Two scenarios are considered which differ only in their treatment of the dimension-six quark condensate (script O sign₆). The first scenario assumes an effective scale for (script O sign₆) from other sum-rule applications which is assumed to be independent of the physical value of the quark mass, while the second scenario requires self-consistency between the value of (script O sign₆) and the current algebra constraint 2m(q̄q) = - f²_πm²_π. Predictions of the pion-resonance mass Mv and decay constant F_π are obtained in these two scenarios. A byproduct of this analysis is a prediction of the renormalization-group invariant quark mass (m̂_u + m̂_d) /2.