Rigourous QCD Evaluation of Spectrum and Ground State Properties of Heavy Quarkonium Systems; with a Precision Determination of the bottom quark mass and of the eta-b mass

Abstract

We present an evaluation of heavy quarkonium states (bottomium and charmonium) from first principles. We use tree-level QCD (including relativistic corrections) and the full one-loop potential; nonperturbative effects are taken into account at the leading order through the contribution of the gluon condensate <alpha_strong G^2>. We use the values Lambda_QCD= 200 (+80/-60) MeV and <alpha_s G^2> = 0.042 +/- 0.020 GeV^4, but we trade the value of the quark mass by the masses of J/psi, Upsilon as input. We get good agreement in what is essentially a zero parameter evaluation for the masses of the 1S, 2S, 2P states of bottomium, the 1S state for charmonium, and the decay Upsilon --> e^+ e^-. As outstanding result we obtain the precise determination of the bottom quark mass (m_b) as well as an estimate of the hyperfine splitting M(Upsilon)-M(eta_b): m_b(m_b^2) = 4387 (+7/-2) (-3/+4) (+16/-32)(systematic) MeV, M(Upsilon)-M(eta_b) = 36 (+13/-7)(+3/-6) (+11/-5)(syst.) MeV, the first error due to that in Lambda_QCD, the second to that in <alpha_s G^2> (varied independently). For the c quark, we find m_c(m_c^2)= 1306 (+21/-34)(-6/+6) MeV (up to systematic errors).