Pion-Nucleon Charge-Exchange Scattering and the Crossover Phenomenon withM=0ρandM=1ρ′Trajectories

Abstract

A Regge-pole model with ($M=0$) $\ensuremath{\rho}$ and ($M=1$) ${\ensuremath{\rho}}^{\ensuremath{'}}$ trajectories is used to fit the $\ensuremath{\pi}N$ charge-exchange differential cross-section and polarization data. The model automatically predicts the crossover phenomenon around $t=\ensuremath{-}0.2$ ${\mathrm{GeV}}^{2}$ in $\ensuremath{\pi}N$ elastic scattering without assuming any zeros in the nonflip $\ensuremath{\rho}$ residue. Thus it avoids difficulties of such zeros due to factorization. The parameters of the $\ensuremath{\rho}$ and ${\ensuremath{\rho}}^{\ensuremath{'}}$ are consistent with the nucleon electromagnetic form factors and predict the mass of ${\ensuremath{\rho}}^{\ensuremath{'}}$ to be around 1.1 GeV.