An effective gauge field theory of the nucleon interactions

Abstract

We discuss the possibility of constructing an effective gauge field theory of the nucleon interactions 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 effective field theory predicts the structure of interactions of protons and neutrons with ρ- and σ-mesons, and with pi-mesons and photons, as well as interactions of these particles with each other. The Lagrangian of the theory consists of several parts involving dimension 4 and 5 gauge invariant operators. Feynman rules for physical degrees of freedom that follow on 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 effective theory is discussed and estimates are made of the resulting coupling constants. The theory predicts the mass of the neutral ρ ⁰-meson to be about 1 MeV larger than the mass of the charged mesons ρ ^±. The vector ω-meson, which is a sterile particle with respect to the considered gauge group SU _I (2) × U _Y (1), can be added to the scheme via a gauge-invariant operator of dimension 5, as shown in the appendix.