Absorption in High-Energy Photoproduction

Absorption in high-energy photoproduction has been derived using a Regge amplitude. It is found that this depends strongly on the square of the four-momentum transfer $t$, smaller values of $\mathrm{}\left|t\right|\mathrm{}$ giving much less absorption. This behavior differs markedly from that of the Drell peripheral model with a constant absorption factor. The absorption is calculated for $s$ and $t$ values corresponding to energies encountered in a recent SLAC experiment, and is seen to reduce the cross section by factors of $\frac{1}{220}$ to $\frac{1}{25}$, depending on $t$. Factors of this order are needed to bring experiment and theory into agreement. The high-energy asymptotic behavior of the amplitude with absorption is found to differ from the usual Regge behavior. The usual absorption using a Born amplitude is also elaborated and generalized and is compared with recent DESY data. The well-known high-energy Regge behavior of the cross section without absorption, $\frac{d\sigma }{\mathrm{dt}}=C\left(t\right)\mathrm{}{s}^{2\alpha \mathrm{}\left(t\right)-2\mathrm{}}$, is derived for all spins in an Appendix.