Regge Poles in Scalar-Vector Field Theory

It is shown that to fourth order, the asympotic behavior of the photon-meson helicity amplitudes in scalar electrodynamics may be viewed as arising from two nearby Regge poles. The photon-meson scattering amplitude is examined to fourth order in the limit $\mathrm{}(-z)\mathrm{}\to \infty$, where $z$ is the cosine of the scattering angle. The two highest powers of $\ln \mathrm{}(-z)\mathrm{}$ are retained. By comparing these forms order by order with those predicted by the presence of two Regge poles, two trajectories are obtained, one of which passes through the meson.