Regge Cuts, Absorption Model, and Diffractive Effects in Inelastic Scattering

Abstract

We propose a model for calculating Regge-cut contributions to scattering amplitudes in terms of a Regge-pole and elastic scattering. Physically, the cuts are caused by absorption effects. Our expression for the cuts contains only one parameter with limited range besides those associated with the Regge pole and elastic scattering. We can explicitly show that combining absorption and Regge poles leads to no double counting. In this model all Regge poles are evasive at $t=0$. This model, with $\ensuremath{\pi}$-exchange input, applied to the forward peaks in $\ensuremath{\gamma}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}n$, $\ensuremath{\pi}N\ensuremath{\rightarrow} (\mathrm{transverse} \ensuremath{\rho})N$, $\mathrm{np}\ensuremath{\rightarrow}\mathrm{pn}$, and $\ensuremath{\pi}p\ensuremath{\rightarrow}\ensuremath{\rho}\ensuremath{\Delta}$, is qualitatively the same as the absorption model, which is successful for these reactions. On the other hand, the conspiring Regge-pole model with factorization fails for $\ensuremath{\pi}p\ensuremath{\rightarrow}\ensuremath{\rho}\ensuremath{\Delta}$. We also apply the model with $\ensuremath{\rho}$-exchange input to ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{\circ}}n$. The dip at $\ensuremath{-}t\ensuremath{\approx}0.6$ Be${\mathrm{V}}^{2}$ in $\ensuremath{\pi}N$ charge exchange is a diffraction minimum which, in the Regge language, is an interference between the Regge pole and the Regge cut. The Regge-pole contribution to the amplitude, taken by itself, has no dip. We predict that the dip drifts to smaller values of $\ensuremath{-}t$ as the energy is raised and the forward peak shrinks. The crossover effect in the ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}p$ differential cross sections is also obtained.