Inelastic Levinson's theorem, CDD singularities, and multiple resonance poles

Abstract

Some effects of inelastic channels on elastic partial wave amplitudes are discussed. A Levinson's theorem for both the real part of the phase shift and the total phase of the elastic amplitude is derived. The CDD singularities required to make the elastic amplitude calculated by single-channel inelastic N D equations agree with the many-channel calculation without CDD singularities are fully characterized in both the η and R methods. Finally, a simple explanation of multiple resonance poles on different Riemann sheets of the amplitude is given in terms of the analyticity properties of η.