EmpiricalNDPotential and Castillejo-Dalitz-Dyson Poles in the Pion-NucleonP11State

Abstract

The CERN phase-shift analysis is used to evaluate the left-cut term of the $P_{11}$ partial wave of pion-nucleon scattering. The inelastic $\frac{N}{D}$ equation is solved with this term and the elasticity $\eta$ as input. The output and input phase shifts agree below 2 BeV if and only if at least two Castillejo-Dalitz-Dyson poles are included in the canonical $D$ function. This result rules out single-channel bootstrap models and furnishes a constraint on many-channel models.