Impact parameters and absorbed Regge poles in inclusive reactions

We derive an impact-parameter representation for inclusive reactions in the fragmentation region. We use this representation to calculate $s$-channel unitarity (absorptive) effects by generalizing the methods which have proved successful in two-body reactions. The resulting procedure is also derived directly, using the technique of eikonal field theory. A general formula is given for absorptive corrections to triple-Regge models. We apply the formula to the reaction $\gamma p\to {\pi }^{\pm }X$, and predict a turnover in $\frac{\mathrm{Ed}\sigma }{d^{3}p}$ at ${p_{\perp }}^2\lesssim 0.015$ Ge${\mathrm{V}}^2$, in contradiction to previous calculations with or without absorption. Direct arguments against the previous calculations are also presented.