Overlapping resonances in multichannel reactions

The existing methods of constructing an explicitly resonance, unitary S matrix are reviewed. These methods can be used for describing groups of resonances r(i) with identical quantum numbers in the case where they overlap, when \E-ri - E-rj\ similar to Gamma(ti) + Gamma(rj). The relation between these methods is studied in detail. The description of excited states by means of the Breit-Wigner formulas is used most often in many problems of resonance physics and nuclear physics, and in this review we focus on the construction of a unitary, T-invariant, multichannel, multiresonance S matrix of the Breit-Wigner type. As a real application of these methods we study the excitation spectrum of vector rho and omega mesons. The possibility of interpreting these as quark-antiquark excited states is discussed. (C) 1998 American Institute of Physics.