A Theorem on Photomeson Production near Threshold and the Suppression of Pairs in Pseudoscalar Meson Theory

It is shown that the photoproduction of charged pseudoscalar mesons at threshold computed to lowest order in the meson-nucleon mass ratio but to arbitrary order in the meson-nucleon coupling constant is essentially equivalent to the weak-coupling result obtained from second-order perturbation theory. The $\frac{\ensuremath{\mu}}{M}$ corrections can be estimated from the ratio of the positive to the negative production cross section. It is therefore suggested that the measurement of the $S$-wave photoproduction of charged mesons may be one of the more reliable methods presently available for determining the meson-nucleon coupling constant. As the threshold production proceeds entirely through the mediation of negative energy states the connection of this result with the possible suppression of nucleon anti-nucleon pairs is discussed.