Final state interaction in the production of heavy unstable particles

Abstract

We make an attempt to discuss in detail the effects originating from the final state interaction in the processes involving production of unstable elementary particles and their subsequent decay. Two complementary scenarios are considered: the single resonance production and the production of two resonances. We argue that part of the corrections due to the final state interaction can be connected with the Coulomb phases of the involved charge particles; the presence of the unstable particle in the problem makes the Coulomb phase ``visible''. It is shown how corrections due to the final state interaction disappear when one proceeds to the total cross-sections. We derive one-loop non-factorizable radiative corrections to the lowest order matrix element of both single and double resonance production. We discuss how the infrared limit of the theories with the unstable particles is modified. In conclusion we briefly discuss our results in the context of the forthcoming experiments on the $W^+W^-$ and the $t\bar t$ production at LEP $2$ and NLC.