Superconvergence relations for $$\overline {\mathcal{N}} + {\mathcal{N}} \to \pi + \rho $$ and $$\overline {\mathcal{N}} + {\mathcal{N}} \to \pi + \omega $$

Abstract

Superconvergence relations for\(\overline {\mathcal{N}} + {\mathcal{N}} \to \pi + \rho \) and\(\overline {\mathcal{N}} + {\mathcal{N}} \to \pi + \omega \) are considered which follow from high-energy behaviour. Saturating these relations with a number of low-lying states we obtain\(g_\varphi {\mathcal{N}}/g_\omega {\mathcal{N}} = 0.06\), andmω=mρ andgρωπ=21 (GeV)−1 in good agreement with experiment. Assuming ρ-meson universality and vector-meson dominance we obtain\(g_\rho {\mathcal{N}} = 2.8,g_\omega {\mathcal{N}} = 6.4,f_\rho {\mathcal{N}} = 10.3\) in agreement, and\(f_\omega {\mathcal{N}} = 4.0\) in disagreement with the results of a least-squares fit of low-energy\({\mathcal{N}} - {\mathcal{N}}\) data.