MatrixNDMethod with Arbitrary Inelasticity

The $\frac{N}{D}$ method for $n$ two-body channels is extended to allow arbitrary inelastic effects. The functions regarded as given are the left-cut discontinuities and the "absorption matrix." (The absorption matrix $F$ is the term of the unitarity condition accounting for transitions between the $n$ channels and any other open channels: $\mathrm{Im}{T}_{+}=T_{+\rho }{T}_{-}+F$.) The procedure is based on a new $D$ matrix, which is defined by means of generalized complex phase shifts. The basic equation is a singular but linear integral equation for ImD. The singular equation is related to an equivalent Fredholm equation. The method may provide a useful general framework in which to discuss absorptive corrections to the peripheral model of high-energy processes. It includes other ways of treating such corrections as special approximations. The technique may also be valuable as a tool in constructing a more rigorous bootstrap theory. A by-product of the investigation is an elegant parametrization of an $n$-channel submatrix of the entire $S$ matrix.