Heavy quarkonia mass-splittings in QCD: test of the $1/m$-expansion and estimates of $<\alpha_s G^2>$ and $\alpha_s$

Abstract

I present a more refined analysis of the mass-splittings between the different heavy quarkonia states, using {\it new double ratios} of exponential moments of different two-point functions. Then, I test the validity of the $1/m$-expansion, extract $\alpha_s(M_Z)=0.127\pm 0.011$ from $M_{\chi_c(P^1_1)} - M_{\chi_c(P^3_1)}$, and provide a new estimate of the gluon condensate from $M_\psi -M_{\eta_c}$ and $M_{\chi_b}-M_\Upsilon$, which combined with the recent estimate from the $\tau$-like decay sum rules in $e^+e^-\rar I=1$ hadrons data, leads to the {\it update average value} $\la\alpha_s G^2\ra = (7.1\pm 0.9)\times 10^{-2}$ GeV$^4$ from the light and heavy quark systems. I also find $M_{\Upsilon}-M_{\eta_b}\approx 63^{-29}_{+51}$ MeV implying the possible observation of the $\eta_b$ in the $\Upsilon$-radiative decay.