Any definitive conclusion concerning whether the $A_2$ is split or not should be based not on the validity of the dipole hypothesis but on the possibility of the interference of two resonances. The constraints of unitarity on a multichannel amplitude with two overlapping resonances have been well studied; however, the simplicity and theoretical interpretation of the Breit-Wigner expression for one resonance is lost here, e.g., in that the partial widths are not simply related to SU(3) couplings. Generalizing a previous result for a single channel, we present a multichannel formalism for two overlapping resonances in which the masses and widths are the usual one-state nonoverlapping or "isolated" quantities. This formalism should be attractive for phenomenological analysis of the $A_2$.

• Received 4 August 1971

DOI:https://doi.org/10.1103/PhysRevD.4.2919