Relating multichannel scattering and production amplitudes in a microscopic OZI-based model

TL;DR

This paper develops a microscopic multichannel model linking scattering and production amplitudes in meson-meson interactions, accurately handling overlapping resonances and thresholds, and confirms standard amplitude relations.

Contribution

It introduces a detailed multichannel framework that explicitly relates scattering and production amplitudes with complex coefficients, extending the isobar model in the small-coupling limit.

Findings

Shared denominator in production and elastic scattering amplitudes

Complex coefficients in linear combinations of matrix elements

Standard amplitude relations are satisfied

Abstract

Relations between scattering and production amplitudes are studied in a microscopic multichannel model for meson-meson scattering, with coupling to confined quark-antiquark channels. Overlapping resonances and a proper threshold behaviour are treated exactly in the model. Under the spectator assumption, it is found that the two-particle production amplitude shares a common denominator with the elastic scattering amplitude, besides a numerator consisting of a linear combination of all elastic and some inelastic matrix elements. The coefficients in these linear combinations are shown to be generally complex. Finally, the standard operator expressions relating production and scattering amplitudes, viz. A=T/V and Im(A)=T*A, are fulfilled, while in the small-coupling limit the usual isobar model is recovered.