<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mi>n</mml:mi></mml:math>Charge Exchange and the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>Regge Trajectory

Finding that the Regge exchange of $\ensuremath{\rho}$ and ${A}_{2}$ fails to describe our ${K}^{+}n$ charge-exchange data at 2.3 GeV/c (the highest energy available to date) when a simultaneous fit is attempted with higher-energy data on ${K}^{\ensuremath{-}}p$ and ${\ensuremath{\pi}}^{\ensuremath{-}}p$ charge exchange and ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\eta}}^{0}n$, we introduce a second, lower-lying $\ensuremath{\rho}$-type trajectory (${\ensuremath{\rho}}^{\ensuremath{'}}$). This also provides a possible mechanism for the puzzling ${\ensuremath{\pi}}^{\ensuremath{-}}p$ charge-exchange polarization. We find that we are then able simultaneously to fit all these data (including the polarization), together with related total cross-section differences up to 20 GeV/c, with a ${\ensuremath{\rho}}^{\ensuremath{'}}$ whose spin-1 mass is 1.0 GeV [perhaps the $\ensuremath{\delta}(965)$?] and whose $t=0$ intercept, 1.1 units of angular momentum below the $\ensuremath{\rho}$, agrees roughly with the ${\ensuremath{\rho}}^{\ensuremath{'}}$ proposed by H\"ogaasen and Fischer to describe forward $\overline{p}p$ and $\mathrm{np}$ charge exchange, where the ($p$, ${A}_{2}$) model also fails. Our $\ensuremath{\rho}$ and ${A}_{2}$ trajectories turn out essentially traditional. In the fit, we permit only small $S{U}_{3}$ breaking between the $K\overline{K}$ and $\ensuremath{\pi}\ensuremath{\pi}(or {\ensuremath{\eta}}^{0}\ensuremath{\pi})$ couplings to the trajectories. We further constrain the fit to obey the sum rule of Igi and Matsuda. In fitting our ${K}^{+}$ data at 2.3 GeV/c, we include a deuteron correction, and employ exact Legendre functions rather than the high-energy asymptotic Regge forms. We offer predictions for higher-energy ${K}^{+}$ charge exchange.