QCD Sum Rules and the Pi(1300) Resonance

Global fits to the shape of the first QCD Laplace sum rule exhibiting sensitivity to pion-resonance [$\mathrm{\Pi }(1300)$] 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 $<O_6>$. The first scenario assumes an effective scale for $<O_6>$ 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 $<O_6>$ and the current algebra constraint $2m<\bar{q}q>=-f_{\pi }^2{m}_{\pi }^2$. Predictions of the pion-resonance mass $M_{\pi }$ and decay constant $F_{\pi }$ are obtained in these two scenarios. A byproduct of this analysis is a prediction of the renormalization-group invariant quark mass $({\widehat{m}}_u+{\widehat{m}}_d)\mathrm{/}2$.