Revisiting gauge invariance and Reggeization of pion exchange

Abstract: The Reggeized pion is expected to provide the main contribution to the forward cross section in light meson photoproduction reactions with charge exchange at high energies. We discuss the Reggeization of pion exchange in charged pion photoproduction with an emphasis on consistency with current conservation. We show that the gauge-invariant amplitude for the exchange of a particle with generic even spin $J\geq 2$ in the $t$-channel is analytic at $J=0$, and that it can be interpreted in terms of the nucleon electric current. This enables us to reconcile the dynamics in the $s$- and $u$-channel, which involves also nucleon exchanges, with the amplitude expressed in terms of $t$-channel partial waves, as required by Regge theory.