Meson-nucleon form factors in a chiral soliton model

Abstract

We investigate meson-nucleon form factors within the framework of a non-linear chiral effective lagrangian which includes pions and vector mesons (ρ and ω mesons) as explicit degrees of freedom. Nucleons emerge as topological solitons. We find meson-nucleon coupling constants quite close to their empirical values as derived from phenomenological one-boson-exchange (OBE) models of the nucleon-nucleon interaction. The range of the form factors corresponds to monopole cut-off masses Λ ∼ 1 GeV, not far from those typically used in OBE potentials. Furthermore, we calculate the spectrum, i.e. the mesonic mass distributions of the various meson-nucleon vertex functions. We find that the spectral distribution of the pion-nucleon form factor is peaked close to μ 2 = ( m π + m π ) 2 ≈ (900 MeV) 2. This suggests that the πN coupling involves dominantly πρ intermediate states, a result which is consistent with dispersion theoretic descriptions of the πNN form factor. Finally, we investigate the spectral functions of our previously calculated nucleon electromagnetic form factors in comparison with those of the related vector-meson-nucleon vertex functions and discuss the range of validity of the vector meson dominance principle.