An effective gauge field theory of the nucleon interactions

Abstract

We discuss the possibility of constructing an effective gauge field theory of the nucleon interations based on the ideas of isotopic invariance as well as hypercharge invariance as a local gauge symmetry and spontaneous breaking of this symmetry. The constructed model predicts the structure of interactions of protons and neutrons with $\rho$- and $\sigma$-mesons, with pi-mesons and photons, as well as interactions of these particles with each other. The Lagrangian of the model consists of several parts parts involving dimension 4 and 5 gauge invariant operators. Feynman rules for physical degrees of freedom as follow from the Lagrangian define the structure of diagrams for one-boson exchanges between nucleons predicting the internucleon one-boson exchange potential as well as nucleon scattering amplitudes. The range of applicability of the model is discussed and estimates are made of the resulting coupling constants. The model predicts the mass of the neutral $\rho^0$-meson to be about $1\,MeV$ larger than the mass of the charged mesons $\rho^{\pm}$. The vector $\omega$-meson, which is a sterile particle with respect to the considered gauge group $SU_I(2)\times U_Y(1)$, can be added to the scheme by means of a gauge-invariant operator of dimension 5, as shown in Appendix ~A.