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Equivalent-potential approach using the bethe-salpeter and unitarity equations

  • Balazs, L.A.P.
Publication Date
Jan 01, 1969
DOI: 10.1103/PhysRev.176.1769
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A Bethe-Salpeter potential is defined which will reproduce the absorptive part at each energy. The method is a straightforward generalization of the one originally proposed by Charap and Fubini for defining the correct nonrelativistic potential. It is, however, fully relativistic and does not seem to lead to spurious singularities. In practice, an approximate version of the potential is used—one which gives only long-range effects correctly. In addition, the absorptive part is assumed to be dominated by a few narrow resonances; a discussion is given of the differences between such an equivalent potential and a potential given by perturbation theory. The method is applied to a rough calculation of the ρ meson in ππ scattering with the potential constructed from ρ, f0, and g meson exchange. Experimental values are taken for their masses as well as for the input ρ and f0 widths. The input g-meson width (which is least well known experimentally) is then adjusted so that the output ρ has the correct mass. This leads to widths of 222 and 175 MeV for the input g and output ρ (compared with experimental values of 170±30 and 125 MeV, respectively). Finally, a purely on-shell technique is discussed which is very similar to the Bethe-Salpeter scheme but may avoid some of its difficulties.

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