Where is the string limit in QCD?

Abstract

The energies of glue in the presence of a static quark-antiquark pair are calculated for separations r ranging from 0.1 fm to 4 fm and for various quark-antiquark orientations on the lattice. Our simulations use an improved gauge-field action on anisotropic space-time lattices. Discretization errors and finite volume effects are studied. We find that the spectrum does not exhibit the expected onset of the universal pi/r Goldstone excitations of the effective QCD string, even for r as large as 4 fm. Our results cast serious doubts on the validity of treating glue in terms of a fluctuating string for r below 2 fm. Retardation effects in the Upsilon system are also studied by comparing level splittings from the Born-Oppenheimer approximation with those directly obtained in simulations.