K+nCharge Exchange and theρ′Regge Trajectory

Abstract

Finding that the Regge exchange of $\rho$ 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 $K^{-}p$ and ${\pi }^{-}p$ charge exchange and ${\pi }^{-}p\to {\eta }^{0}n$, we introduce a second, lower-lying $\rho$-type trajectory (${\rho }^{\prime }$). This also provides a possible mechanism for the puzzling ${\pi }^{-}p$ 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 ${\rho }^{\prime }$ whose spin-1 mass is 1.0 GeV [perhaps the $\delta \mathrm{}\left(965\right)\mathrm{}$?] and whose $t=0\mathrm{}$ intercept, 1.1 units of angular momentum below the $\rho$, agrees roughly with the ${\rho }^{\prime }$ proposed by Högaasen and Fischer to describe forward $\overline{p}p$ and $\mathrm{np}$ charge exchange, where the ($p$, $A_2$) model also fails. Our $\rho$ 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 $\pi \pi (or {\eta }^0\pi )$ 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.