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Three-pion scattering amplitudes and integral equations
Phys. Rev. D 13, 2352 – Published 15 April, 1976
DOI: https://doi.org/10.1103/PhysRevD.13.2352
Abstract
The isospin structure of the three-pion-to-three-pion scattering amplitude is studied using a generalization of the tensor analysis which is well known in two-pion scattering. This leads to a natural definition of the various -to- isoscalar amplitudes, a simple deduction of the consequences of Bose statistics for these amplitudes, and a straightforward technique for carrying out the isospin reduction of the full scattering amplitude and corresponding scattering integral equations without the use of recoupling techniques. Our general results are applicable to a very wide class of three-pion scattering integral equations; however, we only consider in explicit detail the so-called -matrix formalism. A new derivation of the latter is given specifically for -to- scattering in order to illustrate the generation of connected-kernel scattering equations for three identical particles without the usual introduction of (interim) unphysical operators and amplitudes which are defined in terms of the interactions of specific particles.
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