Implications of Regge Behavior for Processes Involving Photons

Properties of the crossing matrix for helicity amplitudes are enumerated and then exploited in a simple Regge-pole model of photon-hadron interactions. We find that: (1) The vacuum or Pomeranchuk trajectory is absent in forward Compton scattering of real photons on nucleons or pions. Thus the total nuclear cross section for photons or nucleons should vanish asymptotically. (2) The amplitudes entering the forward spin-flip Compton scattering of virtual photons on protons, which are crucial in the proton structure contributions to the ground-state hyperfine splitting (hfs) in hydrogen, may be chosen so that they do not require a subtraction when writing dispersion relations for them in the energy variable. One must look elsewhere than to the high-energy behavior of the amplitudes for the erasure of the discrepancy between theory and experiment on the hfs. (3) In forward photoproduction of vector mesons on protons, the polarization of the mesons should be predominantly longitudinal at "high energy." (4) In the differential cross section $\frac{d\sigma }{\mathrm{dt}}$ for photoproduction of neutral pions, there should be a dip at $t\approx -0.5\mathrm{}$ Be${\mathrm{V}}^2$ because of a nonsense zero in all crossed-channel helicity amplitudes.