Pion-nucleon partial-wave analysis with fixed-t dispersion relation constraints.

Abstract

We have performed a set of partial-wave analyses of the pion-nucleon elastic scattering data to 2 GeV employing rigorous constraints from simultaneous forward and fixed-t dispersion relations. Constraints were generated from the forward ${\mathit{C}}^{\ifmmode\pm\else\textpm\fi{}}$ amplitudes and the invariant amplitudes A and B at fixed t in the range 0 to -0.3 ${\mathrm{GeV}}^{2}$. Solutions were generated for a range of pion-nucleon coupling constants (${\mathit{g}}^{2}$/4\ensuremath{\pi}) and isoscalar scattering lengths (${\mathit{a}}^{(+)}$). A chi-squared map for these (${\mathit{g}}^{2}$/4\ensuremath{\pi},${\mathit{a}}^{(+)}$) solutions exhibits a clear minimum near ${\mathit{g}}^{2}$/4\ensuremath{\pi}=13.75 (${\mathit{f}}^{2}$/4\ensuremath{\pi}=0.076) for both the fits to the data and the dispersion relations. While favoring a particular ${\mathit{g}}^{2}$/4\ensuremath{\pi}, this work shows that it is possible to obtain good, stable fits for nearby values, but at the cost of increased chi squared. Consequently, this approach provides a criterion for defining the preferred value and uncertainty of ${\mathit{g}}^{2}$/4\ensuremath{\pi} from pion-nucleon scattering data. On this basis, we conclude that ${\mathit{g}}^{2}$/4\ensuremath{\pi}=13.75\ifmmode\pm\else\textpm\fi{}0.15 (${\mathit{f}}^{2}$/4\ensuremath{\pi}=0.076\ifmmode\pm\else\textpm\fi{}0.001).