Suppression of Pair Effects in Doubleπ-Meson Photoproduction at Low Energies

The matrix element for the photoproduction of a (${\pi }^{+}, {\pi }^{-}$) pair by $\gamma$ rays on protons is examined in the low-energy region. Using the Deser-Thirring-Goldberger definition of the nucleon-meson interaction in a symmetric pseudoscalar theory with pseudoscalar coupling, it is shown that the leading term in an expansion in $\frac{k}{M}$ ($k$ being the kinetic energy of the light particles and $M$ the mass of the nucleon), is exactly the pair-term contribution in the perturbation result ($\sim e{g}^2$), but occurring with the much smaller ${g_s}^2$ coupling constant. With the actual value of the pion mass, terms proportional, for instance, to $\left(\frac{\mu }{M}\right){g_P}^2$ then become predominant.