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Coupled-Channel Amplitudes: Physical Effects and Analytic Structure
Phys. Rev. D 1, 549 – Published 15 January, 1970
DOI: https://doi.org/10.1103/PhysRevD.1.549
Abstract
An investigation is made of the effects of an indefinite number of coupled channels on two-particle amplitudes. Central coupling, chain coupling, and combinations of them are considered. Some results are general, while others depend on a generalized potential model. The existence of strong resonance-producing effects is related to zeros of the matrix. Forms of Levinson's theorem are found for both the amplitude and -matrix phases. It is shown that if the effective number of coupled channels increases linearly with the energy that (1) the partial-wave matrix can vanish asymptotically (the usual result is that ); and (2) Regge trajectories rise asymptotically as the square root of the energy. Special results of the MacDowell symmetry are noted for a finite number of coupled channels. With respect to a special (boundary condition) model it is found that Regge trajectories which cross the origin near should have much larger slopes than those crossing the origin near , in agreement with observation. Regge cuts result from the coupling of effective three-body channels.
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