Bjorken Limit and Pole Dominance. II. VirtualπρScattering

The Bjorken limit and the pole-dominance approximation (PDA) are applied to a study of four-point functions. We consider $I=2\mathrm{}$ $\pi \rho$ scattering and its off-mass-shell extensions. The four-point function obtained using the PDA and unsubtracted dispersion relations is not consistent with the Bjorken limit, and we therefore add contact (direct-interaction) terms. These terms are determined by use of the Bjorken limit and a smoothness postulate. We first include $\pi$- and $A_1$-meson intermediate state and use the result to discuss the ${\pi }^{+}-{\pi }^0$ mass difference for massive pions. We extend the discussion to include $\omega$ contributions and examine some $\pi \rho$ scattering sum rules.