Uniform Treatment of Pion Electro- and Photoproduction in Regge Theory

Abstract

The problems associated with the conventional kinematical interpretation of the pion pole in Regge theory are studied. It is found that a formulation leading to a dynamical interpretation is possible in an approach which emphasizes the Lorentz-invariance interpretation of gauge invariance. This approach leads to a uniform treatment of pion production by real and virtual photons in the sense that the former is demanded to be the zero-mass limit of the latter in a manner consistent with Lorentz-invariance requirements on helicity amplitudes, as suggested by Weinberg. Our formula for the meson Regge pole has a singularity at $t={\mu }^2$ which explicitly comes from a factor $\frac{1}{sin\pi \alpha \mathrm{}\left(t\right)\mathrm{}}$, rather than the kinematical factor ${(t-{\mu }^2)}^{-1\mathrm{}}$ used in recent phenomenological analyses. Comments are made on some features arising from gauge invariance which are analogous to perturbation theory.