Three-Dimensional Field-Theoretical Construction of the Nucleon-Nucleon Potential from Quark Degrees of Freedom

Abstract

Considering nucleons as bound systems of quarks the field-theoretical spectral decomposition for theNNscattering amplitude and the corresponding relativistic three-dimensional Lippmann–Schwinger equation are derived. The resulting equations have the same form as the linearized Low equation without quark degrees of freedom. In the linearly energy-dependent potential of this equation the contributions from meson exchange and quark-gluon exchange can be exactly separated. Some constraints for quark masses and quark-meson vertex function parameters appearing in this general field-theoretical potential are obtained. In particular, it is shown, that if the sum of constituent quark masses is equal to the nucleon mass, i.e.m1+m2+m3=mN, the pure off mass-shell one-meson exchange interaction betweennucleonsvanishes. Furthermore, in this case meson-exchange interactions between quarks appear always together with gluon exchange in the resultingNNpotential. These results may shed further light on the problem of double counting inherent in modernNNpotentials which employ both quark and meson degrees of freedom.