Two-Level Formula for Maximally Overlapping Resonances and Its Application to theA2Meson

A two-level formula for overlapping and inelastic resonances is examined. Detailed discussions are made for the extreme case in which the partial-wave $S$-matrix elements have two poles and two zeros lying on the same vertical line in the complex energy plane. A dipole is also included as a special case. All the important results (some of which look rather strange) are presented in a general and transparent way without using detailed numerical calculations. A peculiar phenomenon suggested by Coulter and Shaw is naturally explained. The formalism is applied to the observed double-peaked structure of the $A_2$. An analysis of the minor decay modes $A_2\to \pi \eta$ and $A_2\to K\overline{K}$ suggests that the choice of two resonances, one narrow and one broad, is somewhat favored over other choices—a dipole and two equal-width resonances.