Abstract
In a crossing-symmetric Regge theory with several coupled two-particle channels, there are many-particle absorptive effects due to crossed two-particle processes. Also, some of the partial-wave amplitudes have overlapping left-hand and right-hand cuts in the $s$ plane. To enforce unitarity in such a theory, one needs a coupled-channel $\frac{N}{D}$ method allowing arbitrary absorption parameters and overlapping cuts. These requirements lead to a nonlinear marginally singular $\frac{N}{D}$ equation, which is proposed as part of a scheme to construct a coupled-channel Regge theory with exact crossing symmetry.
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