0 Vibrating the QCD string

The large-distance behaviour of the adiabatic hybrid potentials is studied in the framework of the QCD string model. The calculated spectra are shown to be the result of interplay between potential-type longitudinal and string-type transverse vibrations. General arguments from QCD and lattice data tell that the theory, even quenched in quarks, possesses nontrivial spectrum, so that effective degrees of freedom for constituent glue should be introduced to describe QCD in the nonperturbative region. As far as we know the possibility for mesons with gluonic lump to exist was first considered in [1] in 1976. Modern wisdom tells that the area law asymptotics for the Wilson loop implies a kind of string to be developed between quark and antiquark at large distances, and it is natural to identify the q ¯ q system connected by the string in its ground state with conventional q ¯ q meson, while the string vibrations are responsible for gluonic (hybrid) excitations. This picture, though physically appealing, does not follow directly from the QCD, and one relies upon models to describe these excitations. There are two main ideas on how to construct such models. One is to consider point-like gluons confined by some potential-type force [2, 3], and another is to introduce string phonons [4]. In principle the best way to discriminate between these two possibilities is to compare predictions with experimental data on hybrid mesons. Indeed, there is a lot of indications that hybrid mesons are already found, but the conclusive evidences have never been presented, nor have alternative explanations been completely excluded [5]. On the other hand, lattice calculations are now accurate enough to provide reliable data on the properties of soft glue and to check the model predictions. In this regard recent measurements [6] of adiabatic hybrid potentials are of particular interest. These simulations measure the spectrum of glue in the presence of static quark and antiquark separated by some distance R. Not only these potentials enter heavy hybrid mass estimations in the Born-Oppenheimer approximation. The large R limit is important per se, as the formation of confining string is expected at large distances, and direct measurements of string fluctuations become available. It is our purpose to investigate the large-distance behaviour of adiabatic potentials in order to establish what kind of the effective string degrees of freedom are excited at large distances.