Sum rules for photoproduction with Boson-Fermion commutation relations

Abstract

Sum rules applicable to the photoproduction of π and η mesons on nucleons are written down using the commutation relation for electromagnetic current density with the field of the proton. These rules relate scattering channels obtained by interchanging a boson with a fermion line, e.g., γ+N→π +N and N+N‾∼ γ+π channels. When saturated with nucleon, N^∗ , S₁₁, and vector-meson poles, these rules relate photonic vertices of the vector meson to the vertices of fermions. Such relations between all boson vertices and fermion vertices are consequences of the boson-fermion commutation relations. The estimate for π ω γ coupling is in agreement with the values obtained from the partial decay width for ω → π γ . The estimate for η ρ γ coupling leads via the ρ -dominance model to a value of total decay width for the η meson in agreement with other such estimates.