Calculation of the first diagonal Padé approximant to π-N elastic scattering with theσ-modelelastic scattering with theσ-model

• DOI: 10.1007/bf02723269
• Publication Date: 2007-12-18T13:30:52Z
• Authors: J. A. Mignaco; E. Remiddi
• Keywords: Coupling constant; Unitarity

The first diagonal (unitary) Pade approximant for elastic pion-nucleon scattering is evaluated within the renormalizedσ-model of Gell-Mann and Levy by computing the perturbativeS-matrix up to 4th order (one-loop approximation). The resulting phase-shifts are studied as a function of theσ-meson mass and the meson-nucleon coupling appearing in the renormalized Lagrangian, which are the only two parameters left free in the theory. Solutions remarkably good for theP33 andS31 waves having also a resonatingP11 are obtained for lowσ masses. For big enough values of that parameter other solutions agreeing with the experimentalS-wave phase shifts up to 1400 MeV of c.m.s. energy are obtained, as is desirable, from the relation between « tree » graph calculations of the model and current algebra. For all interesting solutions the effective pion-nucleon coupling constant lies within 40% of its experimental value, and the pion decay constant obtains somewhat better. However, agreement for all partial waves simultaneously is never achieved and some of the physically small phase-shifts show ghosts when theσ mass is pushed to high values.