The Charmonium Spectrum on the Lattice: A Status Report

This is a status report on our calculation of the charmonium spectrum. Our first results were presented last year [1]. An important aspect of this calculation, the determination of αs from the charmonium spectrum, has already been reported separately [2]. The detailed results of this study will be presented in a future publication [3]. The calculation of experimentally well measured quantities in the charmonium spectrum serves several purposes. The investigation of physical quantities that are sensitive to the systematic errors present in lattice calculations can lead to a better understanding and possibly the removal of these errors. On the other hand, a quantity that is relatively independent of the systematic errors of the lattice calculation can be used to obtain information about fundamental parameters of the Standard Model. In Refs. [1,2] we argued that the 1P-1S splitting falls into the latter class of quantities and therefore lends itself to an accurate determination of the strong coupling constant of QCD. The splitting between the J/ψ and ηc, on the other hand, is expected to strongly depend on the leading lattice spacing errors. This splitting and the leptonic decay amplitude of the J/ψ are expected to also show some dependence on the charm quark mass. One might therefore use these two quantities in a study of the former type. Some of the details of the calculation are described in section 2. The effect of the omission of sea quarks has already been discussed in detail in our analysis of αs. In section 3 we discuss their effect on the hyperfine splitting and the leptonic