The spectrum of the Υ system is investigated using the Nonrelativistic Lattice QCD approach to heavy quarks and ignoring light quark vacuum polarization. We find good agreement with experiment for the Υ, Υ ′ , Υ ′′ and for the center of mass and fine structure of the χ b -states. The lattice calculations predict b b D-states with center of mass at (10.20 ± 0.07 ± 0.03)GeV. Fitting procedures aimed at extracting both ground and excited state energies are developed. We calculate a nonperturbative dispersion mass for the Υ(1S) and compare with tadpole-improved lattice perturbation theory.

Recent results from lattice QCD simulations provide a realistic picture, based upon first principles, of Y physics. %e combine these results with the experimentally measured mass of the Y meson to obtain an accurate and reliable value for the b quark's pole mass. %e use two different methods, each of which yields a mass consistent with Mb = 5.0(2) GeV. This corresponds to a bare mass of Mq = 4.0(1) GeV in our lattice theory and an MS mass of Mb (Mq) = 4.0(1) GeV (MS denotes the modified minimal-subtraction scheme). We discuss the implications of this result for the c-quark mass.

We present an application of the recently proposed method of discretized light-cone quantization to quantum chromodynamics (QCD). We present the general method of light-cone quantization and point out its usefulness for the derivation of covariant integral equations for bound states. We then apply it to QCD and obtain the integral equation for the bound states in the valence sector of the mesons. The numerical solution of the integral equation shows a nice transition to the continuum. The conclusion summarizes the main results and discusses briefly what should be the next improvements of this method.