Diffraction Scattering and Vector-Meson Resonances

Atkinson, D. & Contogouris, A. P., 1968, In : Journal of Mathematical Physics. 9, 9, p. 1489-1500 12 p.

Research output: Contribution to journalArticleAcademicpeer-review

It is shown that, under reasonable assumptions about inelasticity and asymptotic behavior, the usual diffraction picture combined with the N/D approach to π‐π scattering leads to a singular integral equation. The authors' formalism is then used to show that, in conformity with the nearby‐singularities philosophy, a constant left‐hand discontinuity is by itself incapable of producing resonances in the GeV region. Next, a model for the creation of vector resonances, which combines a long‐range force (defined by exchange of a cutoff vector meson) plus a short‐range force (compatible with diffraction requirements), is introduced. The effect of the short‐range force on the self‐consistent (bootstrap) solutions is investigated in an approximate scheme. For a self‐consistent solution with the correct ρ‐meson mass, which is found to exist, inclusion of the short‐range force is shown to decrease the self‐consistent width by a factor of 2, which is nevertheless still greater than the experimental value.
Original languageEnglish
Pages (from-to)1489-1500
Number of pages12
JournalJournal of Mathematical Physics
Issue number9
Publication statusPublished - 1968
Externally publishedYes

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