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 $M_{{\chi }_c(P_1^1)}-M_{{\chi }_c(P_1^3)}$, and provide a new estimate of the gluon condensate from $M_{\psi }-M_{{\eta }_c}$ and $M_{{\chi }_b}-M_{{\rm Y}}$, which combined with the recent estimate from the $\tau$-like decay sum rules in $e^{+}{e}^{-}\text{rar}I=1$ hadrons data, leads to the {\it update average value} $\text{la}{\alpha }_s{G}^2\text{ra}=(7.1\pm 0.9)\times 10^{-2}$ GeV${}^4$ from the light and heavy quark systems. I also find $M_{{\rm Y}}-M_{{\eta }_b}\approx 63_{+51}^{-29}$ MeV implying the possible observation of the ${\eta }_b$ in the ${\rm Y}$-radiative decay.

Comments: Talk given at QCD 96-Montpellier, 4-12th July 1996 and at the 28th ICHEP96-Varsaw, 25-31th July 1996, and based on the paper hep-ph/9512348 (to appear in Phys. Lett.B386, October 1996). 9 pages in Latex files.