Role of complex poles in a fieldtheoretical model for πN scattering
Abstract
The "uncrossed meson line" approximation for the nucleon propagator is appled to the pionnucleon S matrix. The resulting simplification resembles the Born approximation, but with the dressed nucleon propagator of Brown, Puff, and Wilets (BPW), which contains a pair of conjugate complex poles. The complex poles appear naturally in the consistent solution of the factorized BPW equations, and are interpreted according to Lee and Wick as states of indefinite metric. Inclusion of these poles produces considerably closer agreement with experimental results. The AdlerWeinberg consistency condition on pionnucleon scattering is now satisfied to within 20%, and this is reflected in the nearthreshold suppression of the cross sections and amplitudes (nucleonantinucleon pair suppression). The (3, 3^{+}) resonance is absent in the model. The model is most appropriate for calculating the twopion contribution to the nucleonnucleon potential, where subthreshold behavior is more important than the scattering resonances.
 Publication:

Physical Review D
 Pub Date:
 January 1975
 DOI:
 10.1103/PhysRevD.11.110
 Bibcode:
 1975PhRvD..11..110N