Scale of corrections to the t-channel pole approximation in quasielastic pion knockout from a nucleon by high-energy electrons

An investigation of a dominant role of the simplest t-channel pole diagrams in pion electroproduction on nucleons for quasielastic-knockout kinematics at an electron energy of a few GeV is completed-namely, the competition between the t-channel pion and rho-meson pole amplitudes, on one hand, and the s-channel pole amplitude (tree diagram), on the other hand, is considered. When the virtual-photon mass is sufficiently large Q ²>2(GeV/c)²], the last amplitude does not make significant contributions to relevant cross sections, either the longitudinal (dσ _L/dt) or the transverse (dσ _T/dt) one. At Q ²=0.7(GeV/c)², the term associated with the interference between the t-channel pion-pole amplitude and the s-channel pole amplitude is still noticeable in the longitudinal cross section. The vertex functions g _ρ NN(t) as obtained from the cross section for the quasielastic knockout of rho mesons and from the cross section for pion photoproduction are compared. Their disagreement must give impetus to a further development of the gauge-invariant theory of pion photoproduction.