Composite-Particle Scattering in Nonrelativistic Off-Shell Theory

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Abstract
On the basis of the Faddeev equations for three-body scattering amplitudes, the scattering formalism involving composite particles is investigated in comparison with the S-matrix formalism. First, the amplitude is defined by the residue at the poles corresponding to the composite particles in Faddeev's three-body scattering matrix and then the equation for our off-shell amplitude, which was firstly given by Lovelace, is reduced from the Faddeev equations by the simpler and unambiguous way. Unlike the case of the on-shell S-matrix theory, our off-shell “potential” does not give rise to any anomalous threshold, but includes the upper anomaly coming from the three-body unitary cut. In order to obtain the solution satisfying the two-body unitary relations, an off-shell N/D method is introduced. The off-shell formalism obtained here includes the three-body cut more self-consistently and does not require any ambiguous procedure for the treatment of the singularities due to the unstable particles, while the expediential procedure is more or less needed in the S-matrix formalism.

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