Volume 81, Number 6, March 2008
Article Number 61002
Number of page(s) 3
Section The Physics of Elementary Particles and Fields
Published online 25 February 2008
EPL, 81 (2008) 61002
DOI: 10.1209/0295-5075/81/61002

The complex relation between production and scattering amplitudes

E. van Beveren1 and G. Rupp2

1  Centro de Física Teórica, Departamento de Física, Universidade de Coimbra - P-3004-516 Coimbra, Portugal
2  Centro de Física das Interações Fundamentais, Instituto Superior Técnico, Technical University of Lisbon P-1049-001 Lisboa, Portugal

received 30 October 2007; accepted in final form 27 January 2008; published March 2008
published online 25 February 2008

The constraint implied by the unitarity relation $\Im m(A)=T^{\ast}A $ is derived for a three-body production amplitude A that consists of a complex linear combination of elements of the two-body scattering amplitude T. We conclude that the unitarity relation does not impose a realness condition on the coefficients in the expansion of A in terms of T.

11.80.Gw - Multichannel scattering.
11.55.Ds - Exact S matrices.
13.75.Lb - Meson-meson interactions.

© EPLA 2008