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

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

1996-09-05

arxiv.org/abs/hep-ph/9609258v1

Nucl.Phys.Proc.Suppl. 54A (1997) 238-243

Physics

High Energy Physics

High Energy Physics - Phenomenology

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 h

Scientific paper

10.1016/S0920-5632(97)00047-9

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.

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