Two Overlapping Resonances: Production and Decay inS-Matrix Theory

Abstract

We discuss the system of two overlapping resonances along two parallel lines: (A) the general restrictions imposed on the $S$ matrix by unitarity, and (B) the results of the Weisskopf-Wigner approximation. The equivalence between the two is used to get a physical understanding of the formalism applicable to both scattering and decay processes. We show that the connection between the overlap in channel space, ${\chi }_c$, and the overlap of the two resonances, $\chi$, is the unitarity sum rule.