Singularities in the Angular Momentum Plane

Abstract

Evidence for the existence of cuts in the angular momentum plane is discussed and the recent experimental data from CERN on $p\ensuremath{-}p$ scattering are interpreted in terms of a simple model with a Pomeranchuk pole ${\ensuremath{\alpha}}_{p}(t)[{\ensuremath{\alpha}}_{p}(0)=1]$ and a cut extending as far as $\mathrm{Re}\ensuremath{\alpha}(t)=1$ for all $t$. A fit is obtained to the $p\ensuremath{-}p$ data in the region between 3-30 GeV/c and there is a pronounced flattening of the curves for $\frac{d\ensuremath{\sigma}}{\mathrm{dt}}$ above 20 GeV/c, but the total cross section still approaches a constant value and the model yields a shrinkage of the diffraction peak, though more slowly than in the single-pole model without a cut. The presence of a cut also provides a natural explanation of the effects previously attributed to a second Pomeranchuk trajectory. Due to the competition of the cut and the pole near $t=0$ the value of the trajectory ${\ensuremath{\alpha}}_{p}(t)$ cannot be accurately determined for small $|t|$ with the present experimental data, and it is possible that $\frac{d{\ensuremath{\alpha}}_{p}(0)}{\mathrm{dt}}$ is, in fact, much smaller than that obtained from only a pole model and may even be zero. The calculations suggest that more accurate data with $t\ensuremath{\sim}\ensuremath{-}0.8$ are most likely to decide whether Regge poles are the only singularities determining high-energy scattering.