Quantum Chromodynamics and the Nucleon-Nucleon Interaction

Abstract

Quantum Chromodynamics is assumed to be the correct theory for strong interactions. This conviction stems solely from extremely high energy data with momentum transfers of 10 GeV/c and larger where the running coupling constant α _s (q ²) is small and perturbation theory can be used. At low energy hadron and nuclear physics we have a length scale between 0.2 and 20 fin corresponding to momentum transfers of 10 to 1000 McV/c. This means that we cannot use perturbative methods to solve QCD. There are promises that QCD on the lattice could once yield exact results for these low energy data, but at the moment we have not even reliably results with this approach to describe a single nucleon and therefore we are far away to understand with lattice QCD the nucleon-nucleon interation. We propose here by doing an averaging on the lattice to introduce colour displacement fields for the colour electric and the colour magnetic field strength treating the dielectric constant as a dynamical variable which describes collective quantities of gluons (something similar to collective glueballs). These collective glueballs describe then the long range behaviour of the interaction of gluons with quarks. The short range part which cannot be described adequately by averaging over larger areas of the lattice are further described by plain gluons. The theory has similarities with electrodynamics were one also introduces the electric displacement fields as averaged quantities over a large number of atoms which describe smoothly the electric and the magnetic fields which vary strongly at scales of inner atomic distances. The theory yields absolute colour confinement for quarks and gluons. It contains two parameters, the strong coupling constant α _s and the product of a coupling constant connected with the quark mass term g _m multiplied with the mass of the collective glueballs. This two parameters are adjusted to reproduce the nucleon mass and the radius of 0.6 fm of the quark content of the nucleon. Then we calculate parameter free the nucleon-nucleon ¹ S potential. The strength comes out right but the range is slightly too large. This is attributed on one side to the fact that the center of mass corrections are till now only performed for the quarks but not for the collective glueballs and that the model does not yet contain sea quarks. In spite of this minor shortcoming the model gives the most direct bridge between QCD and the nucleon-nucleon interaction which is at the moment available.

Work supported by the Deutsche Forschungsgemeinschaft