Relativistic Quarkonia from Anisotropic Lattices *

The study of heavy quark systems on the lattice is complicated by the large separation of momentum scales which are difficult to accommodate on isotropic lattices. Over the years many effective descriptions of QCD have been developed for low energies and tested against a wealth of experimental data [1–3]. However, the (non-)perturbative control of higher dimensional operators is very difficult and in practise one has to rely on additional approximations. Even in non-relativistic bottomonium calculations one has observed sizable relativistic corrections to the spin structure [4,5] and, more worrying, large scaling violations [6] which cannot be controlled by taking the continuum limit. We take this as our motivation to study heavy quarkonia on anisotropic lattices in a fully relativistic framework. The strategy and first results for charmonium have already been presented in [7,8]. The basic idea is to control large lattice spacing artefacts from the heavy quark mass by adjusting the temporal lattice spacing, at, so that mqat < 1. The continuum limit can then be taken at fixed anisotropy, ξ = as/at. The details of our calculation are given in Section 2. In our study we also employ another advantage of anisotropic lattices a fine temporal resolution is ideal to trace the fast exponential fall-off from