Understanding the residue of theπN3-3 resonance pole

Abstract

The residue of the $\ensuremath{\pi}N$ 3-3 resonance pole (as determined from experimental data by Ball, Lee, and Shaw, who suggested that the results might not be easily explained) can be quantitatively understood in terms of a few simple physical effects. These effects are (1) kinematical effects, such as the threshold factor ${q}^{2l+1}$, (2) real analyticity and unitarity, (3) nucleon exchange, and (4) the opening of inelastic channels at about 1600 MeV. Given the complex mass ($1211\ensuremath{-}50i$) of the 3-3 (deduced from data by Ball et al.), we quantitatively calculate the residue; in particular, the large imaginary part of the residue is correctly given independently of any detailed assumptions.