Closed Regge eikonal formula for summing multiple-Reggeon-exchange contributions to the inclusive six-point function in the fragmentation region

We derive a closed Regge eikonal formula for summing the distinct types of multiple-Pomeron-exchange corrections to the Mueller-Regge contribution to the inclusive six-point functions a + b → c + X in the fragmentation regions. If one takes into account final-state absorption (i.e., Pomeron exchange between c and the missing-mass state X), as Reggeon renormalization to the basic triple-Regge term (Y graph), then using the renormalized Y graph as input, the formula accounts for all the absorptive corrections within a Mueller-Regge framework and essentially can provide a complete description of the inclusive distribution in the fragmentation region. The technique we use is a straightforward generalization of the functional derivative method introduced by Abarbanel and Itzykson for summing multiple-meson-exchange contributions to the four-point function. This generalization allows for a large class of possible nested ladders to be summed up to a closed expression within the eikonal approximation. The formula shows that one should expect the absorption corrections in the case of an inclusive process in the fragmentation region to be much stronger than one would naively expect from the corresponding study of two-body processes