Parameterization dependence of $T$-matrix poles and eigenphases from a fit to $\pi N$ elastic scattering data

We have studied the form dependence of fits to $\pi N$ elastic scattering data, based on a Chew-Mandelstam $K$-matrix formalism. Extracted partial-wave amplitudes and resonances characterized by $T$-matrix poles are compared in fits generated with and without explicit Chew-Mandelstam $K$-matrix poles. Diagonalization of the $S$-matrix yields the eigenphase representation. While the eigenphases can vary significantly for the different parametrizations, the locations of most $T$-matrix poles are relatively stable. We also find the partial-wave amplitudes for $\pi N$ elastic scattering to be quite stable. By turning on and off the explicit Chew-Mandelstam pole contributions, we are able to determine how the $T$-matrix poles are generated in this approach.

Figure 1

Selected partial-wave amplitudes (L${}_{2I,2J}$). Solid (dashed) curves give the real (imaginary) parts of amplitudes corresponding to the WI08 [8] solution. Dash-dotted (dotted) curves give the real (imaginary) parts of amplitudes corresponding to the XP08 solution. (a) $S_{11}$, (b) $S_{31}$, (c) $P_{11}$, (d) $D_{13}$, (e) $F_{15}$, and (f) $F_{37}$. All amplitudes are dimensionless. Vertical arrows indicate Breit-Wigner resonance $W_R$ values, and horizontal bars show full $\Gamma$ and partial widths for ${\Gamma }_{\pi N}$ associated with the GW SP06 solution [7].

Figure 2

Eigenphases. (a) $S_{11}$, (b) $S_{31}$, (c) $P_{11}$, (d) $D_{13}$, (e) $F_{15}$, and (f) $F_{37}$. Upper plots correspond to WI08 solution; lower plots correspond to XP08.

Figure 3

Derivatives of eigenphases. (a) $P_{11}$ and (b) $D_{13}$. Upper plots correspond to WI08 solution; lower plots correspond to XP08.